The Montenegro international escaped ligament damage, but has bruised his tibia and medial meniscus.
In a statement, the Serie A leaders said they expected to be without the 30-year-old for a lengthy period of time.
"Although no surgery is required, the Montenegrin forward is expected to be out of action for several weeks," the statement read.
Behind Carlos Tevez and Fernando Llorente in the pecking order at Juve, Vucinic has largely struggled for game time this season.
He has scored two league goals this season, including the sealer from the penalty spot in Juventus' 3-0 win over fellow contenders Roma in January.
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