The team announced that X-rays on Cano's hand were negative, but that he will have additional tests once the swelling goes down.
The 36-year-old was removed in the first inning after he was struck by an 88-mph fastball thrown by Nationals starter Gio Gonzalez.
Juan Lagares replaced Cano as a pinch-hitter in the at-bat. Jeff McNeil moved to second base to replace Cano in the second inning.
Cano came to the Mets in December 2018 in a deal with the Seattle Mariners that included Edwin Diaz. The Mets in return sent five players to the Seattle.
The veteran second baseman is hitting .270 (27-for-100) this season with three home runs and 11 RBIs in 25 games.
Cano missed a game just over a week ago after he was hit by a pitch on the right wrist.