Inter said Martinez "underwent clinical and diagnostic tests (which) revealed a strain in his left hamstring".
The length of his absence has not been specified, but according to press reports, the Argentine will be sidelined until the next international break.
The 29-year-old forward is therefore set to miss a month of action, including the Milan derby on October 31st.
On Tuesday, Martinez scored two of his team's three goals in a 4-3 defeat to Club Brugge during the second round of the Champions League league phase.
He has already scored four times in the league this season for Inter, who are top of Serie A above second-placed Lazio on goal difference.