Dunn had the appendectomy Tuesday in Kansas City and missed Wednesday's game against the Royals.
The offseason acquisition signed a four-year, $56 million contract with the White Sox. He batted .286 in four games with a homer and five RBIs.
The White Sox also announced they designated for assignment outfielder Lastings Milledge and purchased the contract of right-handed pitcher Jeff Gray from Class AAA Charlotte. Milledge, initially signed to a minor league contract, was 1-for-4 in two games.
Gray is 1-1 with a 4.91 ERA in 36 major league relief appearances with Oakland and the Cubs.
(This version corrects spelling of undergoing in 1st paragraph.)