Bryzgalov, 33, appeared in 20 games this season for Edmonton, going 5-8-5 with a 3.01 goals-against average and a .908 save percentage.
The pick sent to Edmonton was originally acquired last year from Buffalo in the trade that brought first line right wing Jason Pominville to Minnesota.
The Wild (34-21-7), who are battling for a playoff spot, have been plagued by injuries to their goaltenders this season.
Wild general manager Chuck Fletcher referred to Bryzgalov as a "quality veteran who adds depth" in an announcement posted on the team's official Twitter account.
March 4, 2014
Josh Harding has not played since Dec. 31 and has been sidelined indefinitely after undergoing adjustments to his treatment for multiple sclerosis. Niklas Backstrom has been battling an abdominal injury and has appeared in only one game since Jan. 11.
The Wild have benefited from the outstanding play of rookie Darcy Kuemper, who has gone 11-3-2 with a 2.19 GAA in 18 games.
ESPN.com's Pierre LeBrun contributed to this report.