Cano got hurt when he grounded out in the third inning following J.D. Davis' two-out double. The Mets trailed 1-0 at the time.
"He took a few hard steps out of the box, got about halfway down the line and it grabbed on him,'' manager Mickey Callaway said.
An eight-time All-Star, Cano twice failed to run out grounders last weekend against the Marlins in Miami, both of them resulting in double plays. Callaway said he addressed the issue, and Cano did not start Monday against the Nationals.
Callaway cited Cano's hustle when he doubled to right-center as a pinch hitter on Monday night and slid into second.
"I guess he had his fastest time from home to second [in three years], so I'm sure he was aware that he needs to get going a little bit,'' Callaway said.
Cano had an MRI during the game. Callaway said he did not yet know the results.
Mets infielder Luis Guillorme was removed from Triple-A Syracuse's game at Lehigh Valley in the fifth inning, a sign Cano could be headed to the injured list.
"They're always proactive during the game,'' Callaway said. "If something like that happens, they'll pull a player out just to make sure he's good to go in case we need him."