Dybala has eight goals and four assists in all competitions this season and last played in a 1-0 win against Cagliari last weekend.
"Paulo Dybala will undergo surgery in the coming days following an injury to his left semitendinosus tendon," Roma said in a statement.
"The player and the club have mutually agreed that this is the best course of action for an optimal recovery."
Although Roma did not give a timeline for his return, surgery on the semitendinosus tendon usually requires at least three months of recovery.
Roma have been resurgent in Serie A since the arrival of Claudio Ranieri as manager in November, moving up from 12th to seventh in the league as they seek a return to European competition once again next season.
They sit three points behind fifth-placed Juventus and four off fourth-placed Bologna.
They next travel to Lecce on March 29th, after the international break.