According to La Gazzetta dello Sport and Sky Sport Italia, Dybala underwent surgery in Rome on Friday after suffering "a complete longitudinal tear of the external meniscus".
The 2022 World Cup winner cut short Thursday's training session with what Roma initially described as "muscle fatigue".
He is expected to be out for 45 days, which means he will miss seven Italian league matches and the Europa League round of 16 tie against fellow Italian club Bologna.
He did not appear for Roma in February, with the club giving a "knee problem" as the reason. He returned to the bench for the match against Juventus on March 1 but was an unused substitute in a 3-3 draw.
Dybala, 32, lost his undisputed starting position at Roma late last season. In this campaign he has scored only two goals in 17 Serie A appearances.
Roma are fourth in Serie A, 16 points behind leaders Inter Milan, but only two points behind Napoli in third and three ahead of fifth-placed Como.
