The Wild announced the trade Tuesday, one day before the NHL deadline for dealing.
The 33-year-old Russian has a 5-8-5 record in 20 games for the Oilers this season with a 3.01 goals against average. His save percentage is .913. Bryzgalov has 38 games of playoff experience over five postseasons with the Anaheim Ducks, Phoenix Coyotes and Philadelphia Flyers.
The pick sent to Edmonton originally was acquired last year from Buffalo in the trade that brought Jason Pominville to Minnesota.
Rookie Darcy Kuemper has started 15 straight games in goal for the Wild, so Bryzgalov is more for insurance with Niklas Backstrom and Josh Harding not at full strength.