The attackers detonated explosives and fired guns when they invaded the campus, witnesses said, causing some students and faculty to flee, a senior State Department official told CNN.
Three women were among the wounded. According to the Emergency Hospital in Kabul, three people were critically injured, TOLOnews tweeted.
Ahmad Samin, a Chemistry teacher said that he was lecturing when the assailants struck the American University of Afghanistan.
As the attackers opened fire and detonated explosives on the campus, the lights went out in Samin's classroom.
"It was very dark, (and) everyone was running. Everyone started screaming," Samin was quoted as saying.
Amid black smoke, he took off running with the students and other faculty.
Eyewitnesses said they heard gunshots and a blast at 7:50 p.m. local time when students were gathering and eating together.
Ambulances, security forces and rescue teams were on the premises of the university.
According to the Afghan news channel TOLOnews, the gunfire erupted again shortly after the units entered the campus.