"I heard explosions and gunfire is going on close by... our class is filled with smoke and dust," a desperate student told AFP by telephone.
"We are stuck inside and very afraid."
Many other trapped students were tweeting desperate messages for help. Among them was Associated Press photojournalist Massoud Hossaini.
No militant group has so far claimed responsibility for the attack, which comes as the Taliban step up their summer fighting season against the Western-backed Kabul government.
The Italian-run Emergency Hospital in Kabul tweeted that at least five wounded people had been brought to the facility for treatment.
The management of the elite American University of Afghanistan, which opened in 2006 and enrols more than 1,700 students, was not immediately reachable for comment.
The private university is usually packed with students in the evening, many of them working professionals doing part-time courses at the facility.
The assault comes after two professors at the university - an American and Australian - were kidnapped in the heart of Kabul earlier this month, the latest in a series of abductions of foreigners in the conflict-torn country.
It appeared to be the first reported abduction related to a private university in Afghanistan.
The Taliban have stepped up nationwide attacks.
Afghan forces backed by US troops are seeking to head off a potential Taliban takeover of Lashkar Gah, the capital of the southern opium-rich province of Helmand as fighting intensifies.
A roadside bomb killed an American soldier yesterday near the city, and left another American and six Afghan soldiers wounded, the US-led NATO coalition said.
Fighting has left thousands of people displaced in Helmand in recent weeks, sparking a humanitarian crisis as officials report food and water shortages.
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