The 24-year-old Argentine midfielder was forced off just eight minutes before half-time in the win over Atalanta on Sunday.
The injury will see Pereyra miss Argentina’s World Cup qualifiers against Brazil and Colombia next month.
“Diagnostic tests carried out this morning showed a lesion of the second degree of the semimembranosus muscle, with healing time required for about 40 days,” a statement from Juventus read.
