De Rossi, 35, sustained the injury in early stages of Roma's 2-0 Serie A win over Empoli and he played the rest of the match in pain, reports Efe.
Having quit the Italian national team following the failure to qualify for the 2018 FIFA World Cup, De Rossi will try to recover during the international break and be ready for the La Lupa's upcoming games.
After the international break, Roma is scheduled to take on Spal in Serie A action on October 20, three days before playing a UEFA Champions League clash against CSKA Moscow.
The Italian team has yet to announce the estimated recovery time De Rossi would need.
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