Sadaf Khadem and her trainer Mahyar Monshipour are currently in the French city of Poitiers, the spokesperson, who asked not to be named, said.
Khadem, 24, had been due to return to Tehran, where she works as a fitness trainer, following Saturday’s bout in the western town of Royan.
Monshipour, who has double French and Iranian nationality, had been due to make a tour of Iran and give boxing classes.
By taking on 25-year-old Anne Chauvin of France, Khadem defied rules in Iran prohibiting women from taking part in international boxing competitions.
Bare-headed and wearing shorts, she also defied rules in Iran that female athletes should be covered in line with its Islamic laws governing women’s dress.
Khadem is accused of violating Iranian dress rules for women while her trainer is suspected of complicity, the spokesperson said.
Mahyar Monshipour was warned of the existence of the arrest warrant in a text message, said the spokesperson, without giving further details.
The spokesperson said the French sports ministry was aware of the situation and that the two Iranians did not want to speak publicly for now.
“I want to improve as much as possible, go as far as possible and show other Iranian women that they can taste this sport,” Khadem had told AFP ahead of the bout.
Iranian women take part in a variety of sports, including in international competitions, ranging from rowing to rugby to athletics to taekwondo.
However they must always obey Islamic dress rules, which means that some sports such as wrestling, boxing and swimming are off limits in international competition.
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