Police said the teenager had pelted stones at security forces and and set fire to a police building.
Indian security forces have been accused of killing 15 people, mostly protesters, in less than a month in Kashmir, triggering the biggest anti-India demonstrations in the last two years.
Mirwaiz Umar Farooq, a prominent separatist leader who led rallies on Tuesday, called for an end to the "killing of innocent people".
"Protests and civil disobedience will continue until India withdraws its security forces from all populated areas, and punish those found guilty," Farooq said.
"These killings will not deter us from pursuing our goal of independence."
Separatists in Kashmir have fought against Indian rule for 20 years, campaigning for independence or for the region to join neighbouring Pakistan.