The 34-year-old attacking midfielder cut short his holiday in Florida after injuring his right ankle while out jogging, and has already returned to Frankfurt to begin his rehabilitation.
"Alex's injury and lay-off is a big blow for us," admitted Frankfurt sporting director Fredi Bobic. "We wish him a good and quick recovery."
News of Meier's injury comes after it was confirmed that summer signing Carlos Salcedo had picked up a serious shoulder injury whilst on international duty.
Both players are expected to miss the start of the new campaign, the fixture list for which is to be released on 29 June.
Watch: Meier's best goals of 2014/15 when he was the Bundesliga's top-scorer