Witnesses to the skirmishes said police were pelted with stones and bottles, the Russian news agency said.
There was no word of injuries after several thousand people gathered to protest the arrest of Akhmatbek Keldibekov.
Protesters were calling for the resignation of the regional governor if Keldibekov wasn't released.
Keldibekov was arrested last week on embezzlement charges. He denies the charges, saying they're politically motivated.