The veteran striker was withdrawn just after the half-hour mark on Friday, and tests on Monday revealed a hamstring problem in his right leg.
The news is a blow for the Serie A leaders, with their 37-year-old talisman having scored three goals in eight league games this season.
A statement from the club read: "Francesco Totti underwent tests this morning which identified an injury to his hamstring.
"He will be reassessed in 10 days.
"The captain has already begun his recovery programme."
Totti is set to miss four league games - against Udinese, Chievo, Torino and Sassuolo - but should return to action in time for the home clash against Cagliari on November 25.
Roma, who still have a 100 per cent record, hold a five-point advantage over nearest rivals Napoli and Juventus.