"The robot broke the child's finger," Sergey Lazarev, Moscow Chess Federation President, told Tass news agency. "This is of course bad."
A video shared on social media shows the robot taking one of the boy's pieces. The boy then makes his own move, and the robot grabs his finger.
Four adults rush to help the boy, who is eventually freed and ushered away.
Mr Lazarev said the machine had played many previous matches without incident.
The boy was able to finish the final days of the tournament in a cast, Tass reports.