Farkhunda, who was beaten to death by a Kabul mob last week, had been arguing with a mullah about his practice of selling charms to women at a shrine.
In the course of the argument she was accused of burning the Koran and a crowd overheard and beat her to death.
Hundreds of Afghans protested on Monday against the attack.
Farkhunda, 28, was beaten, hit by bats, stamped on, driven over, and her body dragged by a car before being set on fire.
A policeman who witnessed the incident on Thursday told AP news agency that Farkhunda was arguing with a local mullah. Her father said she had complained about women being encouraged to waste money on the amulets peddled by the mullahs at the shrine.
"Based on their lies, people decided Farkhunda was not a Muslim and beat her to death," Mohammed Nadir told AP.
The policeman who saw the incident, Sayed Habid Shah, said Farkhunda had denied setting the Koran on fire.
"She said I am a Muslim and Muslims do not burn the Koran," he said. "As more people gathered, the police were trying to push them away, but it got out of control," he added.
An official investigator has also said there was no evidence she had burned the Koran.
"Last night I went through all documents and evidence once again, but I couldn't find any evidence to say Farkhunda burnt the Holy Koran," General Mohammad Zahir told reporters at her funeral on Sunday. "Farkhunda was totally innocent."
Police say they have detained 18 people over the incident, with more arrests expected. In addition, 13 policemen have been suspended for having failed to do enough to stop the attack.
Shukria, a woman visiting the shrine on Monday, told the BBC that the attack was "not just an attack on Farkhunda, but on all Afghan women. They have killed us all".
Demonstrators have called for justice and planted a commemorative tree.