The indictments follow an investigation launched after images posted on social media networks showed a group of protesters assaulting Basij member Ruhollah Ajamian.
A UK-based activist group says that clashes between protesters and security forces since September 30 in the city of Zahedan have left at least 95 dead, including children.
"The enemy ... wants to pit people against each other," says President Ebrahim Raisi, adding the nation has felt "grief and sorrow" over the woman's death in custody.
In Iran, women are not allowed to watch men's football matches in stadiums, though they have occasionally been allowed to watch volleyball and basketball in stadiums.
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