Kovalchuk registered an assist, two shots on goal and four PIM in Sunday's 4-3 win over the Wild.
Kovalchuk will play alongside Lars Eller and Carl Hagelin on the third line when he makes his Capitals debut Tuesday against the Jets, Samantha Pell of The Washington Post reports.
The Capitals acquired Kovalchuk from the Canadiens in exchange for a 2020 third-round pick.
Kovalchuk had four shots, two hits and one blocked shot in Saturday's 4-3 loss to the Stars.
Kovalchuk scored the overtime goal in Saturday's 2-1 win versus Toronto.
Kovalchuk had an assist and two hits in Sunday's 4-3 loss to the Blue Jackets.
Kovalchuk scored a goal on two shots and added two hits in Thursday's 3-1 win over Buffalo.
Kovalchuk had two goals in a 4-1 win over Philadelphia on Thursday.
Kovalchuk registered an assist and four hits in Wednesday's 4-1 loss to the Blackhawks.
Kovalchuk scored his first goal as a member of the Canadiens in a 2-1 overtime win over the Senators on Saturday.