Sadaf Khadem beat the French boxer Anne Chauvin in an amateur bout on Saturday.
She had planned to fly to Tehran with her French-Iranian trainer this week.
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.
Iranian officials have so far not confirmed the existence of a warrant.
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Khadem fought in a green vest and red shorts with a white waistband – the colors of Iran’s national flag – in Saturday’s bout in the western French town of Royan.
The 24-year-old had to fight abroad as, despite having the blessing of Iranian sporting authorities, it proved too complicated to fulfill their requirement that the bout is refereed and judged by women.
Khadem had been expecting a hero’s welcome when she returned to Iran.
But while she travelled to Paris’s Charles de Gaulle airport with her trainer Mahyar Monshipour – an Iranian-born former World Boxing Association champion who also serves as an adviser to the French sports minister – she said they learnt that warrants had been issued for their arrest.
“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.”
A spokesman for the Iranian embassy in Paris told Reuters news agency that he could not comment on whether Khadem faced arrest in Iran or on her decision not to return to Iran.
Iranian sportswomen are required to cover their hair, neck, arms, and legs when competing.
Until recently, Khadem would not have been permitted to take part in an official boxing match wearing a hijab or a full body form-fitting uniform for religious regions. But the International Boxing Association (AIBA), amateur boxing’s governing body, changed its uniform rules at the end of February.