The woman named Farkhunda was lynched on Thursday by an angry crowd in central Kabul.
"The accusation against her is completely invalid. Farkhunda was a religious girl, she was not involved, she was innocent," interior minister Noorulhaq Ulumi told MPs during questioning in parliament.
"It is very painful that we were not able to protect a pious young person. We hope this will not be repeated again."
Footage of the attack on social media shows several uniformed police watching as the crowd beat 27-year-old Farkhunda to death before burning her body, then dumping it into the Kabul river.
Scores of people protested against the lynching in Kabul today, demanding the government bring the killers to justice.
The protesters marched in front of the mosque and along the river near where Farkhunda was beaten to death.
Farkhunda's body was carried to the graveyard by women amid crowds of men and laid to rest in Kabul yesterday.
