Guerrillas opened fire at the house of Muhammad Akbar Lone in Wagoora village, injuring his 16-year old daughter Shaista and his 8-year old granddaughter, Moomina.
"The two injured girls were immediately shifted to hospital where condition of one of them is stated to be serious," a police officer said.
Senior police officers have rushed to the spot along with reinforcements.
No group has yet claimed responsibility for the attack.
Two sisters were gunned down by guerrillas in the adjacent Sopore town early this month.