Inter confirmed on Thursday that medical tests had revealed a strain in the Argentine forward's left hamstring.
The club have not specified how long he will be unavailable, but reports in Italy suggest he could miss the next month of football.
The injury is expected to rule Martinez out of several important matches, including the Milan derby on October 31.
The 29-year-old picked up the injury after scoring twice in Inter's 4-3 defeat to Club Brugge in the Champions League on Tuesday. Despite his goals, the Italian side suffered a damaging loss in the league phase.
Martinez has been in impressive form in Serie A this season, scoring four goals to help Inter move to the top of the table. They lead second-placed Lazio on goal difference.
