Answering an urgent question in parliament, the Foreign Secretary also played down suggestions that the United Kingdom could give diplomatic status to Nazanin Zaghari-Ratcliffe, who was arrested 19 months ago when she was on holiday visiting relatives in Iran and subsequently imprisoned.
Mr Johnson has faced calls to resign after telling a Commons Committee some weeks ago that Nazanin Zaghari Ratcliffe had been in Iran "training journalists".
Today's meeting will cover Mr Ratcliffe's recent request that the government consider extending "diplomatic protection" to his wife. She was there on holiday.
A Foreign Office statement to the BBC said Johnson and Ratcliffe will meet to discuss a request to give Zaghari-Ratcliffe "diplomatic protection" - which, under global law, allows a state to take diplomatic action on behalf of a national.
Mr Johnson said: "Yes, of course, I apologise for the distress, the suffering that has been caused by the impression that I gave that the Government believed, that I believed, she was there in a professional capacity".
He continued: "I do apologise, I do apologise, and of course I retract any suggestion that she was there in a professional capacity".
Zaghari-Ratcliffe is said to be close to a nervous breakdown.
Her family have always maintained she was on holiday with her daughter.
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He said the suspect has been identified, but his name has not been released pending notification of next-of-kin. The shooter himself has been killed by police and several victims are now being treated at a local hospital.
There have been calls for Johnson to quit in the wake of the gaffe, but Ratcliffe said he should stay and clean up his mess.
Richard would also like to use the meeting to accelerate plans for Mr Johnson to visit Iran after he announced that he would be willing to.
Zaghari-Ratcliffe was arrested in April 2016 as she tried to leave Tehran after visiting her family.
It is thought that legal advice will have to be taken before determining whether the status - which would raise Mrs Zaghari-Ratcliffe's plight from a consular case to a formal dispute between the two countries - is the best method for speeding her release.
Mr Ratcliffe welcomed the opportunity to meet Mr Johnson in person, having only spoken to him over the phone.
Urging Iran once more to release Mrs Zaghari-Ratcliffe on humanitarian grounds, Mr Johnson said: 'Iran's regime and no one else has chosen to separate this mother from her infant daughter for reasons that even they find it hard to explain or describe'.
There are concerns within the Foreign Office that Ratcliffe might still be arrested by the Iranian police, even if he is accompanying Johnson.
Johnson had "made it clear that no stone should be left unturned" in securing her release, the statement added.