Local media said thousands of clerics had gathered at the Loya Jirga tent for the meeting of the Ulema Council, Afghanistan's top religious leaders. No group has claimed responsibility for the attack yet.
Most of the casualties were civilians.
Interior ministry spokesman Najib Danish confirmed it was a suicide attack, and said the bomber had been on foot when he detonated his explosives at the university gate.
Two policemen were among those injured in the bombing, he added.
"There was panic gathering after the explosion", one security offical told Reuters, saying the death toll could rise.
Shortly before the attack, the clerics had issued an Islamic ruling, or a fatwa, declaring that suicide attacks are "haram" - forbidden under Islamic law.
The attack happened at the main entrance of a sprawling compound where about 2,000 Muslim clerics had gathered to deliberate on the current war and attacks by the Taliban and the Islamic State, which are battling the Afghan government and USA and other foreign troops in the country.
He expressed his sympathy with the Afghan government, nation and the bereaved families of the heinous crime and said the establishment of sustainable peace in the war-stricken country depends on unity and vigilance of the government and people from different faiths and ethnic groups. It was the first time the council has issued such an appeal.
"War in its all types is illegal according to Sharia and Islamic laws and it is nothing but shedding the blood of Muslims", the religious scholars said in the fatwa.
The religious scholars repeated their call on the Taliban to accept the Afghan government's "unconditional" peace offer.
The incident is the latest in a string of terrorist attacks to hit the Afghan capital.
The Taliban in April announced the start of their annual spring offensive but in recent years, the insurgent group and also the Islamic State affiliate in the country carry out near-daily attacks through all the seasons. In the rest of the country, Taliban militants are renewing their push for territory against western-backed Afghan troops and ISIS fighters are trying to carve out influence of their own.