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.
Aden McCarthy netted his maiden goal in the UEFA Champions League but it was not enough for his team Sabah as they fell to a 2-1 home defeat against Borussia Dortmund in Baku.
Marc Guehi believes Manchester City can continue to develop under Enzo Maresca as they prepare to face AEK Athens in the UEFA Champions League on Tuesday.
Barcelona midfielder Pedri has jokingly warned his close friend Ferran Torres not to score when the Catalan side face Paris Saint-Germain in a major Champions League clash tonight at Parc des Princes.
Niko Kovac has challenged Borussia Dortmund to end their winless run and rediscover their scoring touch when they face Sabah FK in the Champions League on Tuesday.
