Mr Monshipour, an Iranian-born former boxing world champion who is now a French citizen, set up the bout after Iran opened the door to allowing women to box.
Miss Khadem was quoted by a sports newspaper as saying she believed she was accused of violating Iran’s compulsory dress code by boxing in a vest and shorts.
Miss Khadem, 24, fought in a green vest and red shorts with a white waistband – the colours of Iran’s national flag.
"I was fighting in a legally approved match, in France. But as I was wearing shorts and a T-shirt, which is completely normal in the eyes of the entire world, I confounded the rules of my country," she told the L’Equipe newspaper.
"I wasn’t wearing a hijab, I was coached by a man – some people take a dim view of this."
Hossein Soori, the head of Iran’s boxing federation, denied Miss Khadem would be arrested, attributing the information to "media linked to Saudi Arabia".
"Mrs Khadem is not a member of (Iran’s) organised athletes for boxing, and from the boxing federation’s perspective all her activities are personal," he was quoted as saying by the semi-official ISNA news agency.
Iranian women’s participation in sports events is heavily restricted, though authorities are beginning to give ground in some areas after years of campaigning by pressure groups.
The federation now allows women to register to box, on condition that they be coached by a woman and wear the hijab while competing. To date, no bouts between female fighters have taken place in Iran.
Mr Monshipour was planning to travel back to Iran with Miss Khadem this week.
France’s foreign ministry could not immediately comment on the case.
Franco-Iranian relations are in a tense phase after comments by France’s ambassador to the US last week on Iran’s nuclear programme sparked an angry reaction from Tehran.