About 50 members of the PKK responded by attacking a police vehicle with a Molotov cocktail amid skirmishes that lasted about an hour, the report said.
There was no immediate word on injuries or arrests.
The clash took place in the southeastern province of Sirnak Cizre. The rally was in support of Kurdish fighters in Syria who have been battling a jihadist faction amid Syria's ongoing rebellion.
The demonstrators were part of the PKK's Patriot and Revolutionary Youth Movement, which the Dogan News Agency called a militant youth and public order cadre of the PKK.