Silvestre joined Milan from city rivals Inter on a season-long loan deal with an option to buy in July but is yet to feature for Massimiliano Allegri's side
It is not yet clear how long the 28-year-old will be unavailable for, but Allegri will hope that his return is a speedy one as they aim to build momentum following an indifferent start to the new season.
A statement on the Milan website read: "AC Milan announces that it has not achieved the goals set forth with conservative therapy, today (Thursday) Matias Silvestre has undergone surgery arthroscopic partial meniscectomy in the right knee."
Milan opened their campaign with a surprising 2-1 defeat at Verona, before bouncing back with a 3-1 win over Cagliari at San Siro.
Silvestre's switch to Milan from their bitter rivals came after he endured a disappointing season with Inter, the former Catania and Palermo man making just 20 appearances in all competitions.
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