Kovalchuk, who was traded from the Montreal Canadiens for a third-round pick in the 2020 NHL Draft on Sunday, will play on the third line with Carl Hagelin and Lars Eller.
The Capitals, who are 2-5-1 in past their past eight games, lead the Pittsburgh Penguins by two points for first in the Metropolitan Division.
Winnipeg has lost two straight games after a three-game winning streak. The Jets are one point behind the Calgary Flames and the Arizona Coyotes for the first wild card into the Stanley Cup Playoffs from the Western Conference.
Winnipeg has lost its past seven games in Washington (0-5-2); its last victory was Jan. 22, 2013.