Militants attack American University in Afghanistan, 1 dead
University President Mark English earlier told The Associated Press that security forces had arrived on the scene soon after the attack began around 7 p.m. (1430 GMT), saying "we are trying to assess the situation."
Dejan Panic, the program director at Kabul's Emergency Hospital, said 18 people wounded in the attack, including five women, had been admitted.
Police spokesman Sediq Sediqqi said security forces were conducting a clearing operation to track down the "terrorists."
The university was established in 2006 to offer liberal arts courses modeled on the U.S. system.
The Taliban have been fighting to overthrow the Kabul government for 15 years, and regard foreign civilians as legitimate targets.