The protesters, led by longtime separatist leader Shabir Shah, were taken into custody near a UN observer mission office just before they were about to present a petition to protest alleged brutality by Indian security forces.
The UN office monitors the heavily militarised Line of Control dividing the disputed region into India and Pakistan-held Kashmir.
A police official said protesters were detained to "to preserve law and order" and would be released later.
Authorities threw a cordon of tight security around celebrations marking the Indian national holiday in Srinagar.
Security was tight after police defused four bombs on key highways on Friday.
Other mainly Muslim areas in the state were hit by the strike but the winter capital of Jammu, which is Hindu dominated, was not affected.
Violence in Kashmir has been declining since India and Pakistan began a slow-moving peace process in 2004.
Both nations occupy Kashmir in part but claim it in full but separatists want to break Kashmir away from India and join it to Pakistan, or make it an independent state.
The resistance against Indian rule has left more than 42,000 people dead since it erupted in 1989.