The Taliban authorities have so far said 25 people were killed and 33 others were wounded in the attack.
The Taliban's return to power in Afghanistan last year brought an end to a two-decade war against the Western-backed government, and led to a significant reduction in violence, but security has begun to deteriorate in recent months.
The Islamist hardliners, accused of failing to protect minorities, have often tried to downplay attacks challenging their regime.
Friday's attack triggered sporadic women-led protests in Kabul and some other cities.
Around 50 women chanted, "Stop Hazara genocide, it's not a crime to be a Shiite", as they marched on Saturday in Dasht-e-Barchi neighbourhood where the attack happened.
The rallies have been dispersed by Taliban forces often firing shots into the air and beating protesters.
Afghanistan's Hazaras have regularly faced attacks in the majority Sunni Muslim country.
They have faced persecution for decades, targeted by the Taliban during their insurgency against the former US-backed government and by IS -- both of which consider Shiites heretics.
In May last year, before the Taliban's return to power, at least 85 people -- mainly girls -- were killed and about 300 were wounded when three bombs exploded near their school in Dasht-e-Barchi.
Again, no group claimed responsibility, but a year earlier IS claimed a suicide attack on an educational centre in the same area that killed 24.