The incident took place during a religious holiday outside the holy Mata Vaishno Devi shrine in the town of Katra, The Hindustan Times newspaper reported.
All the injured people have been sent to nearby hospitals.
Police said that the stampede had been caused by an argument that broke out among the pilgrims.
Indian Prime Minister Narendra Modi expressed condolences over the deadly incident.
"Extremely saddened by the loss of lives due to a stampede at Mata Vaishno Devi Bhawan. Condolences to the bereaved families. May the injured recover soon," Modi wrote on his Twitter page.