Police said they did not have permission for the march to Parliament.
The Young India Coordination Committee, which comprises members from various student bodies, had given a call for the march on Tuesday.
"We had submitted the application for permission on February 27. We were informed on Monday about the permission being rejected. It is a last-minute intimation," former JNU Students' Union president N Sai Balaji, who is leading the march, said.
A student said the police were detaining the protesters even if they were assembling in smaller groups. "We will now proceed to Jantar Mantar," he said.