One police official said: "Two of the 13 are in a serious condition … The explosion created panic."
No group has claimed responsibility.
Jammu and Kashmir, the most northern state of India, shares a border with Pakistan to the west and China to the north and the east.
Officials say more than 40,000 people have been killed in Kashmir in the 17-year Muslim separatist revolt against Indian rule.
Human rights groups put the toll at around 60,000 dead or missing.