The Levelling Up Secretary joked after being released from the lift that the incident may have provided inspiration for a new episode of the BBC-based satire W1A.
He was trapped in a BBC lift for more than 30 minutes.
His appearance on BBC Radio 4’s Today programme was delayed as a result of the mishap at Broadcasting House.
Mr Gove told the programme: “After more than half an hour in the lift, you successfully levelled me up, so I’m delighted to be here.”
He acknowledged “these sorts of things happen, and if you and I together have given ammunition for (Thick Of It creator) Armando Iannucci or for the next episode of W1A, then fine.”
Told by presenter Nick Robinson that a “free Michael Gove” hashtag was circulating on social media, Mr Gove said: “I suspect there were rather more people hoping I would be incarcerated for longer.”
Earlier, Robinson had told listeners: “Mr Gove is stuck in the Broadcasting House lift. I wish I could say this is a joke, it is not a joke and it is not very funny for Mr Gove and the security man, who have been stuck there for some time.”
The presenter suggested it was proof that “W1A is not, in fact, a satirical programme”.
The BBC apologised after Michael Gove was stuck in one of the lifts at Broadcasting House.
A BBC spokesman said: “We’re sorry Mr Gove was stuck in one of our lifts, but we’re glad he was later able to take part in the interview.”