Parise sustained bruising and swelling around his eye following a high stick from Washington's Tom Wilson during Tuesday's game. The 32-year-old Parise then fell into the knee of Capitals forward Jay Beagle before hitting the ice.
Parise needed assistance to the locker room and didn't return to the contest, which Washington won with a 5-4 decision. Wilson was given a four-minute, high-sticking penalty.
"His eye looks pretty black and blue, but he can see and he's fine as far as that goes," Boudreau said after Wednesday's practice.
Boudreau said that he doesn't expect Parise to play against the Ottawa Senators on Thursday and admitted he wouldn't be surprised if he sat out the weekend's contests against Nashville and Colorado, respectively.
The Wild signed forward Justin Kloos to a two-year, entry-level contract starting with the 2017-18 season, the team announced.
Kloos, 23, will report to the Iowa Wild of the American Hockey League on an amateur tryout agreement for the remainder of this season.
Kloos recorded 43 points (18 goals, 25 assists), including six game-winning goals and six power-play tallies, in 38 games during his senior season at the University of Minnesota. The two-year team captain led the Gophers in game-winning goals, ranked second in points per game and third in assists and goals during his senior season.
The Toronto Maple Leafs assigned goaltender Garret Sparks to the Toronto Marlies of the American Hockey League.
Sparks, 23, owns an 18-7-0 record with five shutouts, a 2.08 goals-against average and .927 save percentage in 18 appearances for the Marlies this season.
Sparks played in 17 NHL games with the Maple Leafs in 2015-16, posting a 6-9-1 record with one shutout, a 3.02 goals-against average and .893 save percentage. The Elmhurst, Ill., native was drafted by the Maple Leafs in the seventh round in 2011. (Editing by Steve Keating.)