The Serbia international was forced off half an hour into the weekend's 2-1 win over Cagliari and underwent further radiological examinations on Monday, the club said in a statement.
"The tests revealed a high-grade injury to the muscle-tendon junction of the left adductor longus. Further medical consultations will be necessary to determine the most appropriate treatment," Juventus added.
Vlahovic scored twice and got an assist in his last six appearances for seventh-placed Juventus, who are unbeaten in the last seven matches in all competitions. They are trying to erase a five-point gap between them and Serie A leaders Inter Milan.
Juventus host Udinese for a Coppa Italia match on Tuesday, before Sunday's league clash at second-placed Napoli.