The first-place Nationals end a three-game series against the second-place Mets with right-hander Tanner Roark going for his 15th win of the season.
Bench coach Chris Speier will fill in for Baker on Wednesday.
Baker is in his first year as the Nationals skipper and is slated to join the team in Atlanta for a series that begins Friday against the Braves, according to the team.
The Nationals were 86-59 and nine games ahead of the Mets in the National League East heading into Wednesday's game. New York won the division title last year while Washington won the East in 2014 under manager Matt Williams, who was fired after the 2015 season.
Washington has won seven of its last 10 games and has split the first two games of the series with the Mets after New York won 4-3 on Tuesday as rookie T.J. Rivera hit a solo homer in the top of the 10th off Mark Melancon.
Baker has been with the Nationals for every inning this year and has not been ejected, though he came close late in the game Tuesday when he argued a possible strikeout by one of the New York hitters.