Bonucci was forced into action to replace Barzagli after the Juve veteran was stretchered away against Chievo.
"Further examinations at J-Medical today have confirmed the scale of the shoulder inury sustained by Andrea Barzagli five minutes into Sunday's victory over Chievo in Verona," a statement on the club's website said.
"The defender's arm will be in a sling for the next four weeks with a return to action scheduled for approximately for two months' time."
Nicknamed "The Wall', Barzagli fell awkwardly on his arm in an early challenge during the hard-fought 2-1 win at Chievo.
The champions were already without defender Giorgio Chiellini for the trip and had dropped Leonardo Bonucci to the bench after he suffered a thigh injury in a midweek Champions League draw with Lyon.
But Bonucci was forced into action to replace Barzagli after the Juve veteran was stretchered away.
Barzagli, Bonucci and Chiellini -- known as 'BBC' -- also usually play in the same position for Italy, who face Liechtenstein away on November 12 and host Germany in a friendly at Milan's San Siro ground three days later.