With Maicon already struggling with injury, the news that Torosidis requires treatment will see Roma's options at full-back severely limited in the coming weeks.
"Earlier today, Vasilis Torosidis underwent medical tests that revealed a grade-one strain to his right calf," a statement read.
"The player has already started treatment on the injury."
Roma also have Mapou Yanga-Mbiwa and Leandro Castan on the sidelines.
Head coach Rudi Garcia was forced to field forward Andrea Florenzi at right-back in the UEFA Champions League clash with CSKA Moscow on Tuesday, and the 23-year-old could feature there again this weekend against Inter.
Roma will hope Maicon makes a quick return from his hamstring injury to resolve the issue, especially with a crucial Champions League fixture against Manchester City two weeks away.
Maicon did resume training this week, but was not deemed match fit by Garcia for the trip to Moscow.