The MP for Hampstead and Kilburn has been campaigning for the release of Nazanin Zaghari-Ratcliffe, 38, since she was arrested at the airport in Tehran 18 months ago.
In September, the mother-of-one was jailed for five years on allegations of spying and attempting to topple the Iranian regime.
Mrs Zaghari-Ratcliffe had been visiting her parents to introduce them to her daughter, Gabriella.
Earlier this month, she was summoned back to court and threatened with further charges after Mr Johnson mistakenly told a Commons committee that she had been training journalists at the time of her arrest.
Her husband, Richard Ratcliffe, 42, now says his wife is on the edge of a nervous breakdown.
Speaking on BBC Breakfast on Monday, Miss Siddiq called on the Foreign Secretary to “make amends” for his words.
“This issue isn’t political point-scoring for me; this about getting an innocent mother home,” she said.
“I’ve been campaigning on this for 18 months – if Boris Johnson is going to Iran then I have a few demands.
“The first is that he needs to take my constituent, Richard Ratcliffe, with him.
“When he gets to Iran, I want him to meet Nazanin face to face. There’s a history of British diplomats going to Iran, visiting the very prison that Nazanin is in and not getting to meet her.”
She added: “If the Foreign Secretary goes to Iran, meets Nazanin, takes Richard and officially retracts the statement he’s made then at least he’s trying to make amends for what he said.”
She said: “If my constituent spends even one more day in prison as a result of what the Foreign Secretary said then he should resign.”
The couple’s daughter, now three, had her British passport confiscated during her mother’s arrest and has since been in the care of her grandparents in Iran.