Imtiaz Ahmed, a police officer, said: "Two men and three women have died and at least 50 were wounded, some seriously."
The attack took place in Tahab village in the southern Pulwama district, some 40 kilometres south of Srinagar, the capital.
Ahmed said: "The mosque and its surroundings were full of worshippers when the grenade was hurled."
Police said it was not immediately known who carried out Friday's attack but the region has been rocked by a series of grenade attacks in recent months.
The attack was the worst since July when eight tourists were killed and 40 people wounded in Srinagar.
Abdul Jabbar, who witnessed the attack, said the grenade exploded inside the mosque, causing "chaos and panic" among those who had gathered for Friday prayers and a sermon by Abdul Rashid Dawoodi, a leading south Kashmiri cleric.
Another witness, Ashiq Hussain, said the blast occurred when Dawoodi and his followers were entering the mosque.
"The grenade exploded right at the main gate of the mosque, sending splinters in all directions," Hussain said, adding that Dawoodi was among the wounded.
'Act of terrorism'
Javed Mir, a leading Kashmiri political separatist, said: "This is a clear act of terrorism. We condemn it. Whoever has done this can never be a friend of Kashmiris."
In a second grenade attack in Srinagar, four policemen and a woman were wounded, police said.
More than 44,000 people have died in insurgency-related violence in Kashmir, according to Indian records. Separatists say the toll is more than double that figure.
Kashmir is divided between India and Pakistan.
The two have fought two of their three wars over Kashmir, which they claim in full.