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.
And he revealed he had sent a text message to the chairman of the BBC in a bid to speed up his liberation.
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.”
Later, Mr Gove told LBC: “Thanks to the good offices of the Today programme, and also thanks to my texting the BBC chairman, I was liberated.”
He added: “He made sure that a crack engineering team were dispatched. As someone pointed out, even though we had to wait half an hour, eventually I was levelled up.”
He said it was “very good advice from both a health and a safety point of view” to take the stairs out of the building.
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”.
Mr Gove had been touring broadcast studios to talk about the action he is taking to tackle the cladding scandal.