The 31-year-old limped out of Sunday's 3-0 win over Cagliari at the Stadio Olimpico, immediately concerning staff and fans alike.
A club statement on Tuesday confirmed De Rossi is receiving treatment for a grade-one tear to his left calf.
The injury certainly rules De Rossi out of Thursday's trip to Parma and a home clash with Verona at the weekend.
But Roma coach Rudi Garcia will be desperate to have the experienced Italy international back for next Tuesday's UEFA Champions League game away to Premier League champions Manchester City.
With City having lost their Group E opener to Bayern Munich, a positive result for Roma - who began their European campaign with a 5-1 thrashing of CSKA Moscow - would put them in a strong position for qualification.
Roma will go to Juventus five days after that game, with De Rossi likely to be returning to full fitness by then as last season's top two in Italy go head to head in Turin.
