Burks was placed on the 15-day disabled list Monday with a torn left medial meniscus. Tuesday's procedure is arthroscopic.
The Red Sox did not make a corresponding move. They host the Tampa Bay Devil Rays on Tuesday in the opener of a three-game series.
Burks is in his second stint with the Red Sox, for whom he began his major league career in 1987. In nine games, he is batting .133 (4-for-30) with one home run and one RBI.
The 39-year-old has been one of the most consistent hitters -- and injury-plagued players -- in the major leagues during his career. He has 352 homers and 1,206 RBI but has missed at least 20 games 13 times.
Last year, a nerve problem in his right elbow limited Burks to 55 games. He hit .263 with six homers and 28 RBI for the Cleveland Indians, ultimately undergoing surgery in June.
Once a Gold Glove outfielder, Burks has played just 28 games in the field over the last four seasons.
Shortstop Nomar Garciaparra and right fielder Trot Nixon also are sidelined for the Red Sox, who still share the American
League's best record (12-6) following a three-game sweep of the New York Yankees.