Kronwall left Saturday’s game against the New York Rangers after twisting his leg in front of his own net in the second period.
The Swedish blue-liner is Detroit's leader in time-on-ice, averaging 22:28 a game. He has three goals and 17 assists in 53 games this season.
The Red Wings are entering a crucial part of the season, with just a three-point lead over the Philadelphia Flyers for the Eastern Conference's second wild-card spot. The Flyers have one game in hand.
Marchenko, 24, has suited up for 56 games this season, scoring one goal and adding eight assists. He was drafted in the sixth round, 205th overall by the Red Wings in 2011.