The Frenchman, Inter's top scorer in Serie A with 14 goals, is likely to miss Sunday's Serie A match at fifth-placed Bologna, Italian media reported, as the club confirmed Thuram underwent medical tests this morning.
"The tests revealed fatigue in the adductor muscles of his left thigh. His condition will be assessed day by day," Inter said in a statement.
Champions Inter lead the Italian top-flight standings on 71 points after 32 games, three ahead of Napoli.
They host Milan in the second leg of their Italian Cup semi-final on Wednesday, after the first leg ended in a 1-1 draw.
Inter, one of eight teams that have won a league, cup and European Cup treble, could repeat the feat this season.
They face Barcelona, another treble-winning side, in the Champions League semi-finals after advancing to the last four of Europe's elite club competition with a 4-3 aggregate win over Bayern Munich.
Thuram, who has started 26 league games and missed only one this season, recently dropped out of the France squad due to an ankle injury.