Mahsa Amini, 22, was arrested on Tuesday by the special police unit, which is charged with enforcing the strict dress code imposed on Iranian women, such as the obligation to cover their hair.
State television announced his death on Friday after spending three days in a coma.
She was buried on Saturday in her hometown of Saghez in Kurdistan province, according to the Fars news agency.
After the funerals, people “shouted slogans demanding detailed investigations into this case,” according to the same source.
“The demonstrators then gathered in front of the governor’s office” shouting other slogans, before being “dispersed by the security forces who fired tear gas.”
State television showed excerpts from a video on Friday showing a room in a police station where numerous women appear. One of them, introduced as Mahsa Amini, gets up to argue with a “governess” and then collapses.
In another excerpt, the emergency services transport the woman’s body in an ambulance.
Tehran police confirmed her death on Friday and said “there had been no physical contact” between the officers and the young woman.
The Iranian presidency indicated for its part that President Ebrahim Raisi commissioned the Interior Minister to investigate the case.
The head of Tehran’s forensic service said on state television on Saturday that investigations into the woman’s death were underway but would take three weeks.
Mahsa Amini’s death comes amid controversy over the conduct of the morality police, who patrol public spaces to check the application of the veil law and other Islamic rules.
Since the Islamic Revolution of 1979, the law in force in Iran requires women, Iranian or foreign and whatever their religion, to go out with a headscarf.
However, in the last 20 years more and more women in Tehran and other big cities leave a significant part of their hair visible despite the veil.