The 42-year-old closer was carted off the field after twisting his right knee shagging fly balls during batting practice.
Manager Joe Girardi revealed the severity of the injury after the game. Royals team doctor Vincent Key diagnosed a torn ACL after looking at the MRI.
Mike Moustakas matched a career high with three RBIs and made a defensive gem in the ninth for Kansas City, backing a strong start by Danny Duffy (2-2). Jonathan Broxton was helped by two stellar defensive plays to finish for the save.
Rivera was tracking down a ball hit by Jayson Nix in deep centre field when his right knee appeared to buckle a step before the wall. Baseball's career saves leader fell to the warning track and immediately grabbed his knee, briefly covering his face with his glove and grimacing in pain.
Yankees right-hander David Phelps (0-1) allowed two runs and six hits over four innings in his first major league start.
BLUE JAYS 5, ANGELS 0
ANAHEIM, Calif. (AP) — Brandon Morrow pitched a three-hitter for his second career shutout and J.P. Arencibia hit a three-run homer to power Toronto to the victory.
Morrow (3-1) won his third straight start, striking out eight and walking none to help the Blue Jays open an 11-game trip with their fifth win in their last six overall.
Toronto added two more runs on a throwing error by converted third baseman Mark Trumbo.
The only Angels hits were a pair of singles by rookie Mike Trout and a leadoff double in the ninth by Trumbo that ended a string of 14 consecutive batters retired by Morrow.
Dan Haren (1-2) gave up five runs, three earned, and five hits in seven innings for Los Angeles.
INDIANS 7, WHITE SOX 5
CHICAGO (AP) — Jason Kipnis hit a three-run homer and finished with a career-high four RBIs, leading the Indians to the victory.
Kipnis, a native of suburban Chicago, also tripled in a run, walked and scored twice.
Justin Masterson (1-2) picked up his first win of the season, holding the White Sox to three runs over 6 1-3 innings. Masterson improved to 3-1 at U.S. Cellular Field and hasn't allowed more than three runs in any of his six career road starts against the White Sox.
Chris Perez got the last two outs for his ninth save in 10 chances.
White Sox left-hander John Danks (2-4) allowed seven runs, six earned, and nine hits over seven innings.
RAYS 4, MARINERS 3
ST. PETERSBURG, Fla. (AP) — Jeff Keppinger hit a two-run homer and Desmond Jennings added a two-run triple to help Tampa Bay complete a four-game sweep.
Jeff Niemann (2-3) allowed three runs and seven hits over 5 2-3 innings as the Rays extended their winning streak to five with their 11th victory in 12 games.
The Mariners concluded a 10-day, 10-game road trip with a season-high six-game losing streak. The skid came right after a four-game winning streak that included a sweep of Detroit to begin their three-city trip.
The Rays scored all of their runs in the second inning, with Keppinger and Jennings delivering the biggest hits of the day off Kevin Millwood (0-3). Fernando Rodney worked a scoreless ninth inning for his ninth save in nine opportunities.