The Yankees made the move before hosting Boston on Tuesday night.
Ackley is sidelined with a strain in his right lower back and could miss a month, or more if surgery is needed. He was 0 for 3 in two games for the Yankees, and is batting .212 with six home runs and 19 RBIs for the Mariners and New York.
The Yankees recalled right-hander Caleb Cotham from Triple-A Scranton/Wilkes-Barre.
Pineda went on the DL last week with a strain in his right forearm. He is 9-7 with a 3.97 ERA.
Williams injured his right shoulder in June diving into first base on a pickoff try.