Politicians are discussing measures being taken to deal with chaotic scenes at Calais, where large numbers of migrants living in a tent city have attempted to enter the Channel Tunnel.
Mr Farage made the remark during a question and answer session following a speech on the European Union referendum and repeated the suggestion later with reporters.
He said: "It's always possible, isn't it. Let's say I hope it doesn't happen.
"It's important, the Channel Tunnel is important. It's important for trade, it's important for leisure.
"Let us hope those circumstances don't occur - but if the French authorities don't start to take a much stronger and tougher line it is a very real possibility.
"What's happened is all of the emphasis was on the ferry port. If you go back six months, it was the ferry port where the migrants were camped, it was the ferry port where people were attempting to get into lorries and cars.
"Since the massive fencing was put up around the ferry port, it's all moved to Eurotunnel. The weakness of Eurotunnel is however much you build up the security or the fences at the Eurotunnel terminal at Coquelles itself... you go a couple of kilometres down the line and find fencing that is frankly pretty easy to clamber under."
He added: "The risk of the Channel Tunnel being closed doesn't come from here, it doesn't come from Dover, but it does come from France and the French authorities. I very much hope it does not happen."
Speaking later to reporters, Mr Farage was told Al Murray, who ran against him in South Thanet at May's election, had promised voters he would brick up the Channel Tunnel as part of his joke manifesto.
The Ukip leader said: "If the French don't get a grip, it may happen anyway - that's the point. The problem isn't in Dover, the problem is in Calais and it's virtually lawless over there. It's frightening.
"When I drive through there, I feel I'm big enough and ugly enough to look after myself but it's pretty intimidating.
"Who knows, Al Murray may have a future."
Meanwhile, Mr Farage - and David Cameron - have both used the word "swarms" to refer to migrants at Calais.
"A couple of times I've been stuck on the motorway surrounded by swarms of potential migrants to Britain and once they tried the back door of the car to see whether they could get in," the Ukip leader said on ITV1's Good Morning Britain today.
"I kept the door locked. I wasn't getting out. It is really, at times, quite frightening and certainly at night you get the feeling, 'I just want to leave this place as quickly as possible'."
David Cameron's description of migrants has been condemned as "disgraceful" by one of the front-runners for the Labour leadership.
Speaking during a visit to Vietnam, Mr Cameron told ITV News that the problem had become worse in recent months because "you have got a swarm of people coming across the Mediterranean, seeking a better life, wanting to come to Britain".
Labour leadership candidate Andy Burnham was swift to condemn the remark with a statement on Twitter: "Cameron calling Calais migrants a 'swarm' is nothing short of disgraceful. Confirms there's no dog-whistle these Bullingdon Boys won't blow."
Acting Labour leader Harriet Harman said the Prime Minister appeared to want to whip people up against the migrants.
She told BBC News: "He should remember he is talking about people, not insects.
"I think it's a very worrying turn that he appears to be wanting to be divisive and set people against, whip people up, against the migrants in Calais when what he should have been doing, and should have been doing months ago and was warned to be doing, is to get the situation sorted out with the French."
Ms Harman dismissed calls for the British Army to be sent in to sort out the problem.
"I don't think there should be any question of us sending in our army. The French themselves have got troops as well as a large police force."