The strikes happened on the day Afghanistan marked the 101st anniversary of its independence.
Sixteen others were wounded as rockets were fired from two cars in 16th and 17th districts, the Interior Ministry said.
The rockets hit houses in districts 1, 2, 8, 16, Tariq Arian, a spokesman for the Interior Ministry, said on Wednesday. Earlier, he said that the rockets hit districts 1, 2, 10, 16 and 9, most of which struck homes.
The three deaths from the attacks including two government employees. Those injured included six civilians with four children and a woman among them.
Two suspects were arrested from PD 17 of the city in connection with the attacks, Arian said.
A source said that one of the rockets landed in the parking lot of the presidential palace compound, injuring at least seven people.Islamic State militant group claimed responsibility for the attacks.