Beckham, who was visiting Shanghai in his role as ambassador to the troubled Chinese Super League (CSL), expressed hope that the injured would recover quickly after the event had to be called off.
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.
"Nearly 1,000 spectators charged to open the gate at the same time, causing a stampede," the newspaper said on its microblog.
Two students, including a Japanese exchange student, also sustained minor injuries, police said.
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An AFP photographer saw a woman with an injured leg and a uniformed policewoman bleeding.
The policewoman had blood covering her face and looked dazed. Among those attending to her was a man wearing a replica of Beckham's old Manchester United jersey, with the footballer's name and the number "7" on the back.
In a posting on his new account on Sina Weibo, China's equivalent to Twitter, Beckham apologised for the event's cancellation.
"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," he said.
"I heard there were a few injuries, hope the fans are ok and I wish them a speedy recovery," he added.