The designation is retroactive to Monday for Cortes, 28, who is 5-2 with a 5.16 ERA through 11 starts.
A first-time All-Star in 2022, Cortes has struck out 59 batters, walked 19 and allowed 10 homers in 59⅓ innings this season.
The Yankees recalled southpaw Matt Krook from Triple-A Scranton/Wilkes-Barre in a corresponding transaction.
Krook, 28, has been pitching in the minors since 2016 and has yet to make his MLB debut. He is 1-1 with a 1.47 ERA in 13 relief appearances this season for the RailRiders.
Yankees put P Nestor Cortes on 15-day IL with rotator cuff strain