Green isn't expected to be cleared for contact activities for a month, league sources said.
Green was elbowed in the Grizzlies' opener on Friday night, and he went down with a serious injury in the team's home opener for the second straight year.
The loss of Green clears the way for Memphis to move rookie Jaren Jackson Jr. into the starting lineup. The No. 4 overall pick already has shown star potential. Jackson, a 6-foot-11 power forward, had 24 points, seven rebounds and two blocks in the Grizzlies' victory over Atlanta on Friday night.
Jackson is 19 years old, having left Michigan State after his freshman season.
Green, 28, averaged 10.3 points and 8.4 rebounds in 55 games for the Grizzlies last season.