The defenseman appeared to injure his leg when he checked Wild forward Matt Boldy before limping off the ice in the first period of a 5-1 loss in Game 3 on Friday.
"It's lower body, it's going to be some time," Blues coach Craig Berube said Saturday. "It's unfortunate, like I said, but we've got to try and do what we can do and control what we can control. Guys got to go in there and do the job."
Krug was the third defenseman for the Blues to be injured in as many games.
Nick Leddy sustained an upper-body injury in Game 1, a 4-0 win for St. Louis. Although he was able to finish that game, he was replaced in Games 2 and 3 by Calle Rosen.
Robert Bortuzzo sustained an upper-body injury when he appeared to be hit by a shot near his head in the first period of Game 2, a 6-2 win by Minnesota. He was replaced on Friday by Marco Scandella, who missed the Blues' final regular-season game and the first two against the Wild because of a lower-body injury.
However, Leddy and Bortuzzo each took the ice for a full practice on Saturday and could be available Sunday.
"Well, it's good," Berube said. "We'll see how they do on the ice today. I can't answer that question now. We'll see how they do after the skate here."
It would obviously be a boost for the Blues should one or both be available.
"Guys are pushing obviously and we'll see what's going to happen," Blues forward David Perron said. "We'll worry about that tomorrow."
Defenseman Scott Perunovich is also a possibility to play for the first time since he sustained a left wrist injury on Jan. 15 against the Toronto Maple Leafs that required surgery March 9. He was quarterbacking one of two power-play units with defenseman Justin Faulk not skating due to rest, and was activated from injured reserve Sunday.
"He's a possibility right now too," Berube said of Perunovich. "He can move the puck and moves well. It was good to see him, he's back and ready to go if we need him. We'll see.
"He hasn't played games in a long time. It was good that he could run that power play with Krug out right now. We'll see how that goes. He needs some reps. It was one of the reasons we wanted to get out there today too."
Jordan Binnington will start in goal for the first time in the series after Ville Husso started the first three games.
Husso had a 37-save shutout in Game 1 but has allowed nine goals on 59 shots in Games 2 and 3.
"I think he's done a pretty good job for us," Berube said of Husso. "We allowed them to have some odd-man rushes in the game. That's tough, we've got to do a better job there. We can't give up odd-man rushes like that in the game."