The Rocket Man singer also said that legislation would "sail in" if put to a public vote. But Mr Donaldson hit back and said it was up to the Executive to decide what was best for Ulster.
"Elton John is entitled to his opinion, but the reality is that we have a mandate to govern and we have to make decisions based on what we believe is best for Northern Ireland," he added.
"The devolution settlement respects that degree of autonomy and therefore these matters should be decided at Stormont, not elsewhere."
Northern Ireland politicians voted on same-sex marriage for the fifth time on Monday, with a majority of MLAs voting in favour for the first time.
But there will be no change in the law after the DUP used a controversial petition of concern to scupper the move.
Speaking during the debate, Paul Givan, the DUP chair of the Justice Committee, categorically ruled out same-sex marriage.
He said: "For as long as our party has the ability to control things on the Executive, there will not be legislation."
It means that Northern Ireland remains the only part of the UK not to have legislated for same-sex marriage.
When asked about the issue yesterday on BBC Radio 4's Today programme, Sir Elton said: "If it can be voted for in southern Ireland by two to one, it's not the public vote, it's by the politicians - and the politicians need to get their act together and enter the 21st century."
"I'm sure if there was a vote for the public, it would sail in, as it would in Australia."
Upon confirming he would perform a gig here, Sir Elton added: "I'm not a politician, but I will speak out for rights as and when I can, and I'll speak about lesbian, gay, bisexual and transgender (LGBT) rights as I'm an elderly gay citizen."
John O'Doherty from the Rainbow Project, a LGBT support organisation, welcomed the veteran singer's intervention, adding that the issue had received "international attention".
"Poll after poll has shown that the majority of people in Northern Ireland support the introduction of equal marriage," Mr O'Doherty said.
"The majority of our Assembly members have voted in support of equal marriage but, unfortunately, the leadership doesn't exist within Stormont to achieve it at this time."
The Alliance Party's Trevor Lunn - who was once opposed to same-sex marriage but has since been persuaded that it is an equality and not a faith issue - said he agreed with Sir Elton that people were in favour.
"The opinion polls indicate that the public in Northern Ireland is ready for this," he added.
Patrick Corrigan, Northern Ireland programme director of Amnesty International, said Sir Elton was "absolutely right that most people in Northern Ireland back same-sex marriage".
He added: "Politicians who continue to block progress must wake up and realise the damage they are causing to gay people in Northern Ireland, as well as to our international reputation."
On Monday next week, a court case will being brought by two residents of Northern Ireland who have been lawfully married in England but whose marriage is only recognised as a civil partnership here.
Then, in December, a second case will seek to overturn the ban on gay couples getting married here.