Levan Gachechiladze, an opposition leader, was wounded after a rubber bullet hit him in the head.
There are reports that Gachechiladze's brother, Giorgi has been detained.
According to Georgian media, Giorgi triggered the clash by climbing onto the fence of a police compound. Protestors reportedly used sticks to attack the police.
Yekaterina Zguladze, a deputy interior minister, accused opposition supporters of breaking the law.
"This is a hideous violation of the law, an attack on the police. The police are remaining calm protecting the perimeter of the police building. The rally has not been dispersed," she told the Rustavi-2 TV channel.
Giorgi Khaindrava, one of the opposition leaders and former supporter of president Mikheil Saakashvili, said over 60 protesters were hospitalized with various injuries. "I know that 60 people were injured," he said.