The attackers then took refuge in a kitchen, where one detonated a bomb while the other two were killed by security forces, he said.
The attack came as mosques around the city were crowded for a night of religious observances as part of the Islamic holy month of Ramadan.
Kabul's Shi'ite minority have been targeted by suicide bombings in the past. An attack on a Shi'ite mosque in November killed more than 30 people.
Islamic State militants claimed responsibility for that attack, as well as an attack last July that killed more than 80 people at a mostly Shi'ite demonstration.
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