Ammar Qurabi of the Arab Organisation of Human Rights in Syria (AOHRS) said a crowd rioted on Monday after police prevented them from holding a celebration to mark the 25th anniversary of the Kurdistan Workers Party (PKK).
"About 35 people were arrested after hurling stones at the police and damaging property and vehicles in Ain al-Arab," Qurabi told reporters on Tuesday. "The police did not use firearms, but they used tear gas after the violence started."
Qurabi said the violence subsided after the arrests. "AOHRS condemns the use of violence by any entity ... emphasises the importance of national unity and urges self restraint," his rights group said in a statement.
In June, Syria sentenced three members of the PKK to jail after convicting them of seeking secession.
Damascus banned the PKK after a stand-off with Turkey over the group's activities in 1998.
Syria and Turkey came to the brink of military confrontation before Damascus met a Turkish request to expel PKK leader Abdullah Ocalan. Ankara had repeatedly complained that Syria was backing PKK rebels fighting in southeast Turkey.
The two neighbours have improved ties in recent years. Both worry that Kurdish autonomy in northern Iraq could strengthen separatist aspirations among their own Kurdish minorities.
Several banned Kurdish political groups in Syria, which has an estimated two million Kurds, demand the right to teach their language, and citizenship for about 200,000 stateless Kurds.