Video report by ITV News correspondent Joe Pike
The former leader of the House of Commons said that she "smoked weed at university and have never smoked it again since".
Her admission in an interview with the Independent comes after Mr Gove said he "deeply regrets" taking cocaine on "several occasions 20 years ago.
In an interview with the Daily Mail, the Environment Secretary said his Class A drug taking was a "mistake".
It comes after fellow Tory contender Rory Stewart apologised for smoking opium at a wedding in Iran.
“At the time I was a young journalist. It was a mistake. I look back and think ‘I wish I hadn’t done that’.”
He added: “It was 20 years ago and yes, it was a mistake. But I don’t believe that past mistakes disqualify you.”
“The question now is that people should look at my record as a politician and ask themselves ‘is this person we see ready to lead now?’,” he said.
Leadership rival Dominic Raab said the admission was not a reason to see Mr Gove barred from the race.
He told BBC Radio 4's Today show: "I rather admire his honesty."
Mr Raab, who has previously admitted taking cannabis as a student, added: "It was a long time ago and pretty few and far between. I have never taken cocaine or any class A drugs."
He said class A drugs "are a bit different" but went on: "I'm not going to cast any further aspersions on Michael or anyone else who is just honest about being human and doing the things that some young people do - not everyone, obviously - and holding their hand up and saying 'I got that wrong, move on'."
Labour leader Jeremy Corbyn said of the latest drug-taking revelations that he was "unconcerned" about Mr Gove's past life.
Asked whether he had taken drugs in the past, Mr Corbyn said: "No, I've led a very normal life in many ways."
Mr Gove's admission comes after International Development Secretary Rory Stewart said he had smoked opium in Iran - which he described as a "very stupid mistake and I did it 15 years ago"
He said: "I actually went on in Iran to see the damage that opium was doing to communities.
“I’ve seen it as a prisons minister. It was something that was very wrong, I made a stupid mistake.
“I was at a wedding in a large community meeting and somebody passed this pipe around the room and I smoked it – I shouldn’t have done, I was wrong.”
Meanwhile, the race to succeed Theresa May as Prime Minister has stepped up a gear following the submission of her resignation on Friday.
Education Secretary Damian Hinds has given the Gove campaign a boost by lending his support – becoming the second Cabinet member to back the Environment Secretary.
He told The Times: “The next prime minister has to do two sets of things.
“First: deliver Brexit, craft our new relationship with Europe and set our place in the wider world.
“Second: construct a compelling domestic agenda for the whole UK, that spreads opportunity, grows wages and continues the improvement of our public services.
“Michael Gove has the mix of abilities to do both.”