Both players suffered knocks in the 1-0 success on Sunday, which was Roma's first triumph at Perugia in 28 years.
Chivu incurred a muscular sprain while Brazilian midfielder Emerson collected a shoulder injury.
Emerson's injury was not serious enough to prevent him completing the full 90 minutes but Roma are awaiting the results of a scan on the problem.
Romanian defender Chivu's condition is of greater concern as he was forced out of the action at the interval at Perugia.
He is unlikely to play against Milan in the Coppa Italia in midweek but could be out for longer if tests uncover a strain.
