Ayatollah Fazel Lankarani was one of a number of conservative clerics and politicians to argue that it is un-Islamic for women to attend men's sporting events.
Another cleric, Ayatollah Nasser Makarem Shirzai, said it was not safe for women.
The order would overturn a ban stretching back over 25 years on women attending soccer matches.
Ahmadinejad justified his decision on the grounds it would help bring morality and chastity to public places.
RFE/RL Iran Report
SUBSCRIBE For regular news and analysis on Iran by e-mail, subscribe to "RFE/RL Iran Report."