Danks, 31, was winless in 2016, allowing 18 earned runs in 22 1/3 innings and had a 7.25 ERA. Erik Johnson will replace Danks in the starting rotation.
Danks has been with the White Sox for his entire 10-year career and is in the final year of a five-year, $65 million contract.
After his debut in 2007, Danks won 12-plus games three consecutive seasons. He is 79-104 with a 4.38 ERA in his career.
Johnson is expected to start Thursday against the Boston Red Sox.