Parise will accompany Minnesota as it begins a four-game road trip against its Central Division rival, and could play as early as Saturday against the Tampa Bay Lightning.
Kuemper has a mild concussion, and will not travel with the Wild.
Kuemper missed the Wild's game on Tuesday, a 3-1 win against the Detroit Red Wings, with an upper-body injury.
Parise, who left practice early on Sunday with an undisclosed injury, played in the win on Monday against Detroit, skating 18:04 and taking three shots on goal. Head Coach Mike Yeo said he expects Parise to practice on Wednesday before the Wild travels to St. Louis to begin a four-game road trip, while he's still waiting on a more definitive update on Kuemper.
It's been unseasonably warm in Minnesota to kick off winter, making outdoor hockey rinks, a cold-weather staple for the State of Hockey, harder to come by.
Everything on Tuesday though, from light snowfall to the balmy 20-degree temperature was perfect as the Minnesota Wild held an outdoor practice in Edina in front of 1,000 fans.
"It's been tough this year, not a lot of outdoor hockey, but the weather is certainly looking like it's changing its mind, and starting to bring what it's supposed to bring this time of year," Head Coach Mike Yeo said. "I'm sure the outdoor rinks will get going; I know the lakes are starting to freeze."
Forward Kirill Kaprizov (2015 Draft, fifth round) had an assist, as Russia defeated Belarus 4-1 at the IIHF 2016 World Junior Championship on Tuesday.
Kaprizov also had a shot on goal, and recorded at least a point for the second consecutive game after he recorded two points in a 6-4 comeback win on Monday against Finland.
His latest point, against Belarus, came on Russia's game-opening goal. Kaprizov had the secondary assist on a Maxim Lazarev power-play goal.
Dubnyk had left the Wild's practice early on Sunday after taking a shot off his right arm and sustaining a pressure cut that required six stitches.
Head Coach Mike Yeo said he did not know if Dubnyk would back up or not after morning skate on Monday.
Forward Kirill Kaprizov (2015 Draft, fifth round) had a goal and an assist to help lead Russia in a comeback, 6-4 victory against Finland on Monday at the World Junior Championship.
Trailing 1-0 in the first period, Kaprizov scored a power-play goal, his first of the tournament, to tie the game at 1-1.
Finland, the host country, would score the next two goals to take a 3-1 lead, but Russia would stage another comeback. Russia scored four times over the final 11:12 of the second period, with Kaprizov picking up a primary assist on the eventual game-winning goal, to take a 5-3 lead.
Darcy Kuemper will start in goal for the Minnesota Wild on Monday when it hosts the Detroit Red Wings.
It will be Kuemper's fifth start and sixth appearance in the Wild's past 11 games. Kuemper has seen increased playing time due to injuries sustained by starter Devan Dubnyk, but the 25-year-old backup is also playing himself into a more regular role.
So while Dubnyk is a little banged up, it was very possible Kuemper was going to make his ninth start of the season against Detroit regardless.
Defenseman Louis Belpedio scored with 3:18 left in the third period to break a 2-2 tie and help lift the United States past Canada at each team's opening game of the 2016 IIHF World Junior Championships on Saturday.
Belpedio, a third-round selection by the Minnesota Wild in the 2014 draft, is serving as an alternate captain for the United States in his first year participating in the international tournament.
The game, which saw five lead-changes, had the United States gets its second and final lead of the day when Belpedio's point shot was deflected by a Canadian defenseman and scored to make it 3-2 United States.
The Minnesota Wild will make two changes to its lineup on Tuesday when it hosts the Montreal Canadiens.
Erik Haula, who has been a healthy scratch the past three games, will draw into the lineup for the first time since Dec. 15, when the Wild defeated the Vancouver Canucks 6-2. Each player, according to Head Coach Mike Yeo, has been performing well, making the decision to use them on Tuesday easier.
Minnesota Wild prospect Louis Belpedio was named an alternate captain for the 2016 United States Junior National Team for the upcoming 2016 IIHF World Junior Championship in Helsinki, Finland.
A sophomore defenseman currently playing at the University of Miami Ohio, Belpedio also was a captain for the 2014 United States National Under-18 team that won a goal medal in Lappeenranta, Finland at the IIHF Under-18 Men's World Championship.
"We're excited about our leadership group here in Finland," said Ron Wilson, head coach of the team, according to a release from USA Hockey. "Zach (Werenski), Louie, Auston (Matthews) and Colin (White) have led by example since day one in Lake Placid this August and have the respect of everybody in the room."