Cano, 36, ran hard to first base after hitting a chopper to second off Nationals starter Max Scherzer in the third inning, but he pulled up short about three-quarters of the way down the line.
Manager Mickey Callaway went to check on him in between innings, and Cano exited.
Twice last weekend, Cano failed to run out grounders at the Miami Marlins, both of them resulting in double plays.
Callaway, who had defended Cano after Sunday’s game, on Monday called it “unacceptable” and said it was one of the reasons Cano was not in the lineup Monday night.
Cano is batting .241 with three homers and 13 RBIs. The eight-time All-Star was acquired by New York from the Seattle Mariners in December.
Adeiny Hechavarria came on in the fourth inning to replace him at second.
The Associated Press contributed to this report.