The Environment Secretary said he used the drug 20 years ago and branded it "a mistake".
It comes after fellow Tory contender Rory Stewart apologised for smoking opium at a wedding in Iran.
Mr Gove told the Daily Mail: "I took drugs on several occasions at social events more than 20 years ago.
"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."
Speaking to Sky News last week, International Development Secretary Mr Stewart said: "I think it was a very stupid mistake and I did it 15 years ago, and I actually went on in Iran to see the damage that opium was doing to communities."
He added: "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."