Gen. Mohammad Zahir, director of the criminal investigation division, said police were trying to assess why the fight that broke out in the afternoon, killing one student and wounding six others.
An Associated Press reporter at the scene said Shia and Sunni students started fighting and by evening, several hundred more people joined the melee, fist-fighting and throwing stones at each other. He said eyewitnesses at the scene said the clash was related to Ashoura, the commemoration of the 7th century death of the Prophet Mohammad's grandson.
Afghan leaders went to the site to try to calm the crowd. Abdul Azim Nurbakhsh, a spokesman for the Ministry of Higher Education, said late Saturday that classes at the university had been canceled for the next 10 days. Damage was reported to buildings at the university.
Other gatherings marking Ashoura in the Afghan capital were peaceful, but last year, a suicide bomber on foot struck worshippers at a Shiite shrine in Kabul, killing at least 80 people. Some Sunni extremists consider Shiite ceremonies to be heretical.
Separately, NATO said a service member with the international military coalition was killed Saturday in an insurgent attack in the south.
No other information was disclosed.
So far this year, 379 NATO service members have died in Afghanistan.
Associated Press Writer Massieh Neshat in Kabul contributed to this report.