The Wild announced the trade on 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 Anaheim, Phoenix and Philadelphia.
The pick sent to Edmonton was originally acquired last year from Buffalo in the trade that brought Jason Pominville to Minnesota.