The stampede occurred when hundreds of students and spectators tried to rush onto the grounds of the football pitch at Tongji University in northeastern Shanghai, the Xinmin Evening News said.
The former England captain was scheduled to play with the university's team and the youth team of a local football club.
"I had an incredible response from everyone at Shanghai Tongji University today. Sorry I couldn't get out on the pitch to see the teams. It was impossible to get through the massive crowds," Beckham said.
"I heard there were a few injuries, hope the fans are ok and I wish them a speedy recovery," he added.