Jeremy Clarkson faces the possibility of police action after the "unprovoked" attack on a colleague that left them in hospital and ended his BBC career.
Director-general Tony Hall said the Top Gear presenter's attack on producer Oisin Tymon meant "a line has been crossed".
A BBC report found the 30-second attack, which was only stopped when a witness intervened, was accompanied by a volley of verbal abuse so loud it could be heard throughout the hotel where the programme's crew were staying.
It said Mr Tymon, who was left with a split lip after being struck by Clarkson, "believed that he had lost his job" following the attack and drove himself to a "nearby A&E department for examination".
A spokeswoman for North Yorkshire Police said the force had asked the BBC for its report on the incident which happened at a hotel in the county
She said: " The information will be assessed appropriately and action will be taken by North Yorkshire Police where necessary.
"It would not be appropriate for North Yorkshire Police to comment further at this time."
Mr Hall, who said he had met and spoken to both men, said the BBC needed "distinctive and different voices" but not "at any price".
He said: "Common to all at the BBC have to be standards of decency and respect.
"I cannot condone what has happened on this occasion. A member of staff - who is a completely innocent party - took himself to Accident and Emergency after a physical altercation accompanied by sustained and prolonged verbal abuse of an extreme nature.
"For me a line has been crossed. There cannot be one rule for one and one rule for another dictated by either rank, or public relations and commercial considerations."
The BBC investigation found that Mr Tymon was "subject to an unprovoked physical and verbal attack by Jeremy Clarkson".
It said: "V erbal abuse was directed at Oisin Tymon on more than one occasion - both during the attack and subsequently inside the hotel - and contained the strongest expletives and threats to sack him. The abuse was at such volume as to be heard in the dining room, and the shouting was audible in a hotel bedroom."
Mr Hall said "no blame" was attached to Mr Tymon, who, he said, "behaved with huge integrity throughout" and the producer himself paid tribute to the man who attacked him.
Mr Tymon said: "I've worked on Top Gear for almost a decade, a programme I love. Over that time Jeremy and I had a positive and successful working relationship, making some landmark projects together. He is a unique talent and I am well aware that many will be sorry his involvement in the show should end in this way."
Clarkson and his co-hosts, James May and Richard Hammond, were scheduled to take part in four live Top Gear shows in Norway this week, but it was announced on Sunday that they had been postponed.
All three men's contracts run out at the end of this month and Hammond and May's future is still unclear, though Mr Hall said the BBC wanted to "renew" the show for next year.
Speaking outside his home, May said Clarkson's departure was a "tragedy".
He said: " I'm sure Top Gear will continue in some way. It existed before us and it has been reformatted several times."
Asked if he will stay at Top Gear, May said: "Erm, well, I don't want to talk about that too much but I think we are very much the three of us as a package. It works for very complicated reasons that a lot of people don't fully understand. So that will require a lot of careful thought."
Hammond said he was "gutted at such a sad end to an era" after Clarkson's sacking. He added: "We're all three of us idiots in our different ways but it's been an incredible ride together."
The BBC declined to comment on the future of the other two men.
Clarkson changed his Twitter profile to: "I used to be a presenter on the BBC2 motoring show Top Gear."
Clarkson's next step is unknown but it is understood at least one major broadcaster - Sky - has ruled out signing him up.
A spokesman for ITV said they would not comment on "a BBC issue", but a Channel 4 spokesman said: "We have no plans to work with Jeremy Clarkson."
Downing Street said Prime Minister David Cameron, a personal friend of Clarkson, believes that "if you do something wrong at work there can be consequences" and that "aggressive and abusive behaviour is not acceptable in the workplace".
An official statement from James May's agent said: " James was disappointed to hear that the BBC will not be renewing Jeremy's contract, however understands that it will have been a difficult deliberation all round and respects the decision.
"As to the future of Top Gear, it existed before its current format and will no doubt continue to do so. James' involvement in that future requires much thought, deliberation and conversation between many people, and at this moment further speculation on that is not useful.
"James will be making no further comment at this time."
The BBC's creative director Alan Yentob confirmed that Clarkson would continue to be employed until his contract expires at the end of the month and said he wanted Hammond and May to continue to work on Top Gear.
He said Mr Hall was "shocked" by the content of the report on Clarkson's actions, adding: "I do know that this was a very difficult decision for Tony Hall to make.
"I know that he was saddened to have to make it but he felt he had no choice in the circumstances."
Mr Yentob told BBC Radio 4's PM programme: "I know that the circumstances which he reviewed and the incident and what happened were things that shocked him and he felt it couldn't be sustainable."
He clashed with presenter Eddie Mair over whether Clarkson should have been instantly dismissed rather than not having his contract renewed "when he has already suffered, he has lost his job".
"Don't be ridiculous," Mr Yentob said. "Yes, this man carried out a physical assault. Yes, he is employed. His contract is not being renewed and if you are talking about two or three days, when he is anyway in suspension - he is not actually working for the BBC - if you think that is shocking, Eddie you are kidding me."
Turning to the future of Top Gear's other presenters May and Hammond, Mr Yentob said: "I very much hope that they are going to stay with the BBC and stay with Top Gear.
"I think that conversations will go on in the next few days and weeks about the future of the programme."
He added: "If Jeremy is not in it and Richard and James are, that needs to be a conversation with them as well. They need to be happy about what's going on and where they think the programme needs to be."
Clarkson made his first public appearance after learning his contract will not be renewed by the BBC.
He left his upmarket west London home on a push bike wearing a black leather coat and a grey beanie hat.
Riding past photographers and TV cameras, he said: "Excuse me gentlemen, thank you."
Asked by reporters what his reaction was, Clarkson said "I'm off out, sorry" before riding away.
Mr Yentob said he would not rule out Clarkson making a return to the BBC in future.
"Of course I wouldn't rule that out, but that's not for now," he said.
Mr Yentob told BBC2's Newsnight that a decision to extend Top Gear's run to 12 shows may have been a mistake.
"The decision to extend, to do the run of 12 at once, was the decision of the team. In retrospect, was it the right decision? Well, that's a question that you would have to say probably it wasn't the right decision.
"Whether it would have led to these events is speculative. It's very difficult to say why this happened. Clearly, workload is one thing, the stress of the year, all the rest of it."
It was "perfectly natural" for Hammond and May to have reservations about continuing Top Gear, he acknowledged.
"It's perfectly natural for them. They are a team they have worked together for a very long time, they are all very attached. The question of what happens next for Top Gear is a conversation which must go on between the controller of BBC2 Kim Shillinglaw, between Andy (Wilman - producer of Top Gear) and the team."
He said Top Gear may continue if the other presenters quit but "it would be a disappointment to us obviously, to put it mildly, if that happened".