The Nerazzurri striker went for an MRI scan after feeling discomfort during the goalless draw with Shakhtar Donetsk on Tuesday.
Inter confirmed the Belgium international has strained a muscle in his left thigh and that "his condition will be monitored daily".
Lukaku is expected to sit out the Serie A match against Parma on Saturday and is reportedly likely to miss next Wednesday's visit to the Santiago Bernabeu.
The news is a blow to head coach Antonio Conte, whose side have drawn each of their opening Group B matches with Borussia Monchengladbach and Shakhtar.
Lukaku has scored nine goals in 11 appearances in all competitions this season.