The Mexico international sustained the problem during his country's 3-3 friendly draw with Belgium on Friday night, with the injury marring his 100th international appearance.
'Chicharito' is unlikely to be available for Mexico's second friendly of the international break, a clash with Poland in Gdansk on Monday, with national team boss Juan Carlos Osorio admitting that he was unsure on the severity of the issue.
"They're being observed and we don't know the seriousness of the injuries," Osorio told reporters.
Hernandez' injury will also come as a major blow to new West Ham boss David Moyes who is set to take charge of the Hammers for the first time when they travel to Watford next weekend.
The 29-year-old is the Hammers' top scorer in the Premier League this season, netting over a third of their goals to date, and his potential absence will do nothing to boost a team currently languishing in the relegation zone.