“The player and the club have mutually agreed that this is the best course of action for an optimal recovery,” AS Roma said in a statement.
“Wishing Paulo a speedy recovery - we look forward to seeing you back soon!” it added.
The forward injured the semitendinosus tendon of his left thigh during his side’s 1-0 home win over Cagliari on Sunday.
The 31-year-old came off 13 minutes after taking the field as a second-half substitute.
He has been central to Roma’s rise up the Serie A table to seventh place since Claudio Ranieri came out of retirement to return as coach in November.
When Ranieri returned, Roma were just four points above the relegation zone.
ANSA