Koivu announced Friday that he was ending his attempts to play in the Olympics. He has been out since sustaining a broken ankle during a game Jan. 4.
"I'm not going to the Olympics games this year," Koivu said in a statement released on the Wild's official Twitter feed. "I just don't feel healthy enough to feel that I can play at the level that I want."
He said he will take a few days off and then resume skating prior to the Wild getting back together Feb. 19.
Koivu, the captain of the Wild, likely would have held the same role for Finland in Sochi. It would have been the third Olympics for Koivu. The 30-year-old has eight goals and 27 assists in 44 games this season.
Finland also learned Friday that Filppula will miss the Olympics due to a non-displaced fracture in his right ankle. The injury is expected to sideline him for 2-3 weeks.
He sustained the injury during the Lightning's 4-1 loss Thursday to the Toronto Maple Leafs. The center was playing in his second game since returning from a lower-body injury that forced him to miss one game.
It would have been the second Olympics for Filppula. He helped Finland win the bronze medal in at the 2010 Vancouver Olympics with an empty-net goal that capped a 5-3 win against Slovakia in the third-place game.
"I was really looking forward to going to play in the Olympics. I don't really know what to say, it's tough right now," Filppula said. "Something positive is that it's not too bad of a break, so I should be back pretty soon after the Olympics."
In the absence of star forward Steven Stamkos, Filppula has emerged as the team's No. 2 scorer with 20 goals and 41 points in 56 games.
There is no word yet on who will fill the spots left by Koivu and Filppula. The reserves on Finland's roster are Sean Bergenheim of the Florida Panthers and Jarkko Immonen, who plays for Torpedo Nizhny Novgorod of the Kontinental Hockey League.