The Syrian Kurdish internal security service, known as the Asayish, said tensions erupted late Tuesday when a drunk regime fighter began shooting at Kurdish traffic police in the city of Qamishli.
He was arrested along with nine other pro-regime fighters, it said.
But when the National Defence Forces, a pro-regime militia, arrested two Asayish members early Wednesday, "a clash took place between the two sides," it said.
One member of the Asayish was wounded and the Kurdish forces arrested 11 members of regime militias, the statement said.
Qamishli, in Hasakeh province, is under the shared control of the Syrian regime and Kurdish authorities, who have declared zones of "autonomous administration" across parts of north and northeast Syria.
Syrian troops and seasoned Kurdish fighters have coordinated on security in Hasakeh province where Islamic State group jihadists have tried to advance.
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But tensions have built up between the sometimes-rival authorities, often over the government's military conscription.
"Recently, the Syrian government's authoritarian practices towards unarmed citizens have increased... under the pretense of recruitment and military conscription," the Asayish statement said.
Syria's Kurdish authorities announced autonomous rule in areas including Hasakeh province in 2013.
Both Syria's government and Kurdish forces have military conscription, and residents have complained of having to do compulsory service twice.
The Syrian Observatory for Human Rights, a British-based monitoring group, said at least three Kurdish fighters were in regime custody and an unidentified number of government troops were held by the Asayish.
Observatory head Rami Abdel Rahman said the tensions began when the governor of Hasakeh was briefly detained on Tuesday night by Kurdish forces.
"The arrests back and forth have been continuing until today," he said.