A group of tourists was boarding a bus in Gulmarg when suspected Muslim militants threw the grenade, a senior police official said.
One of the injured is in a critical condition.
The Gulmarg valley lies close to the line of control dividing Indian and Pakistani Kashmir.
Muzaffar Beigh, the state tourism minister, said: "These attacks are being carried out by fundamentalist terrorists who have no rules."
He said the attacks were intended to damage the region's economy, which relies heavily on tourism.
Officials say that more than 300,000 tourists have visited Kashmir this year, after a record number of more than 600,000 last year.
The attack came the day after a series of grenade explosions in Srinagar, Kashmir's summer capital, killed nine people, including eight tourists.
Violence has increased in the state in recent months as the snows melted on mountain passes, allowing militants to move more easily from Pakistani territory, Indian security officials say.
Kashmir is divided between India and Pakistan, but both claim the entire region.