Asked about Johnson's comments that supporters of Iranian-British aid worker Nazanin Zaghari-Ratcliffe said could hand her a longer jail term, Gove told the BBC's Andrew Marr show: "There is no reason, no excuse and no justification for her detention and she should be released".
Ms Zaghari-Ratcliffe insists she and her young daughter were just on a family visit when she was arrested in Tehran in 2016.
Johnson was criticised for incorrectly stating that Zaghari-Ratcliffe was in the country in a working capacity.
They hauled her in front of a court last week to confirm she was facing new charges of "propaganda against the regime" and could see her original five-year sentence doubled.
The Iranian government accused her of working for a United Kingdom media network involved in activities against Iran. "Iran. It should be the actions of their judiciary and the revolutionary guards".
Johnson's blunder has triggered calls for his resignation.
The Foreign Office confirmed that Johnson talked to Zaghari-Ratcliffe's husband, Richard, on Sunday, but did not elaborate further, AP reported.
He was defending the foreign secretary, whose own comments have caused concern that her sentence could be extended.
The two agreed to meet in person over the next few weeks.
He will also "look seriously" at the prospect of him accompanying the Foreign Secretary to Iran, and "consider personally" Mrs Zaghari-Ratcliffe's eligibility for diplomatic protection.
Mrs Zaghari-Ratcliffe's family have issued a statement about her condition, saying she had been "complaining of sharp stabbing pains in her breasts" for more than a year.
Beleaguered British Prime Minister Theresa May has been urged to sack her Foreign Secretary Boris Johnson over his handling of the Nazanin Zaghari-Ratcliffe affair.
The family believe the move, based on a legal opinion they submitted to the foreign office two months ago, could aid Britain's efforts to secure her release under global law.
Mr Gove told Andrew Marr he would "take her husband's assurance" that the British-Iranian citizen was on holiday.
That the Foreign Secretary added to her despair by mistakenly telling MPs she was training journalists in Iran is - in the eyes of many - a sackable offence.
"We make a big mistake if we think the right thing to do is to blame politicians in a democracy who are trying to do the right thing for the plight of a woman who is being imprisoned by a regime that is a serial abuser of human rights", he said.
"Her husband said she was there on holiday, and her husband is the person who should know".
"For Michael Gove to go on TV today and say he wasn't sure ... he should know that Nazanin was on holiday and in compounding the lie that was told about training journalists, he is only going to make life worse for my constituent". "It's a Government of incompetence".
Writing in the Observer on Sunday, Corbyn took aim at Johnson, calling for him to be relieved of his duties after "undermining our country" and "putting our citizens at risk".