The attack took place on Tuesday in Pahalgam, a popular destination in the scenic Muslim-majority territory, that draws thousands of visitors every summer as militant violence has reduced in recent years.
The injured had been rushed to a local hospital, the source said on the condition of anonymity as they are not authorised to speak to the media.
Indian TV channels reported earlier that one person was killed and seven injured in the attack.
The Himalayan region, which is claimed in full but ruled in part by both India and Pakistan, has been roiled by militant violence since the start of an anti-Indian insurgency in 1989.
Tens of thousands of people have been killed, although violence has tapered off in recent years.
Attacks targeting tourists in Kashmir have been rare in recent years, but not unknown.
The last major attack on visitors in the federal territory took place in June when at least nine people were killed and 33 injured when a bus carrying Hindu pilgrims plunged into a deep gorge after militants attacked it.
India revoked Kashmir's special status in 2019, splitting the state into two federally administered territories - Jammu and Kashmir and Ladakh.
The move led to a downgrading of ties with Pakistan, which also claims the region.
