The facility, which opened Thursday, is named after Sahar Gul, a teenager police said was found severely beaten in her husband's home, the Voice of America reported. The girl had accused her husband and in-laws.
A VOA report said women were seen crowding around the donated computers in the new Internet facility, run by an Afghan activist group called YoungWomen4Change.
The report said women visiting the center can get on the Internet and exchange information without worrying about men watching them.
"We are very pleased that we are inaugurating this cafe, which is located in a safe location and safe environment," said Eqlima Muradi. "This paves the way for women to come to our cafe and use our facilities."
Naming the place after Sahar Gul is seen as a way to honor her bravery and to show how proud other women are of her and others in similar circumstances, the report said.
In the 1990s, when the Taliban regime controlled the country, women were not allowed to work, get an education or leave their homes without a male escort.