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The draw was made in Nyon on Monday afternoon, with the Giallorossi finding out which former Champions League side they will have to beat in order to reach the last-16 of the competition.
Jose Mourinho's side will face the Austrian champions in the New Year, with the first leg taking place in Salzburg on February 16.
The second leg, at the Stadio Olimpico, will follow a week later on February 23.
The tie will be the first time the two sides have faced each other in European competition.
Tickets for the home match are set to go on sale soon.
Salzburg came third in Group E of the Champions League this season, adrift of group winners Chelsea and runners-up AC Milan.
In two meetings with AC Milan, the Austrian side drew 1-1 at home and then lost 4-0 at the San Siro on the final matchday of the group.
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