The 28-year-old left-hander was transferred to the 60-day injured list Friday. Sidelined by rotator cuff inflammation, the 2022 All-Star is eligible to be activated Aug. 4.
Cortes last pitched May 30 and is 5-2 with a 5.16 ERA in 11 starts. He is expected to throw to hitters Sunday and then again at the Yankees' complex in Tampa, Florida, on July 13.
New York activated left-hander Carlos Rodon from the 60-day IL before Friday's series opener against the Cubs, and he was to make his Yankees debut. Signed to a $162 million, six-year contract, Rodón had been sidelined since spring training by a strained left forearm and bad back.
New York placed infielder/outfielder Jake Bauers on the 10-day injured list because of a bruised left rotator cuff, a move retroactive to Thursday. Infielder-outfielder Franchy Cordero was recalled from Triple-A Scranton/Wilkes-Barre.