The incident occurred in the Anantnag district where security forces resorted to "various crowd control measures" against the rally, Press Trust of India (PTI) news agency reported citing a police official.
Besides, clashes reportedly took place in the Shopian district where protesters threw stones at a police post. Nobody was reported to be injured in the incident.
Authorities extended curfew in some areas of the northern state, in other parts there are restrictions on assembly of four or more people.
The region of Kashmir has been disputed by India and Pakistan since the dissolution of British India and the establishment of the two states in 1947. Some local residents, especially those residing in the Kashmir Valley, call for greater autonomy or even independence from India.