Crawford went 13-for-22 over the week with a double, three home runs and six RBIs. He also posted a 1.045 slugging percentage and scored eight runs.
Crawford had two terrific series, going 5-for-8 with two home runs against Toronto before going off against Baltimore, batting 8-for-14 with a home run.
Crawford, who is hitting .303 with nine homers and 60 RBIs, has shared this award once before, as he and Justin Verlander of Detroit were named Co-Players of the Week on May 29 in 2006.
Cano had a four-hit game against the Kansas City Royals in the Yankees' most recent series and was 11-for-23 (.478) with a slugging percentage of 1.087 and on-base percentage of .556.
He scored nine runs, drove in nine runs and had three doubles and three homers to go along with a triple.
This is the second time in the last three weeks that Cano has been named Player of the Week, sharing the honor with Crawford's teammate, B.J. Upton, for the week ending July 23.
Cano is hitting .309 on the season and has 11 home runs to go along with 63 RBIs. This is the third time he has been presented with the award.
Two of Cano's teammates, Bobby Abreu and Jorge Posada, received consideration, as did Boston's David Ortiz, Baltimore's Aubrey Huff and Chicago's Jermaine Dye.
Pitchers that drew some attention were Scott Baker of the Twins, Erik Bedard of the Orioles and John Lackey of the Angels.
Torneau, the world's largest watch store, will supply Cano and Crawford with luxury Swiss Torneau timepieces in recognition of their achievements.
Matt Smith is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.