Fasth was hurt Monday morning in practice with a possible sprained neck.
Fasth has a 2-1-1 record with the Oilers with a 2.76 goals-against average and an .899 save percentage. He was traded from Anaheim to Edmonton on March 4.
Before the trade, Fasth had a 2-2-1 record with the Ducks with a 2.95 GAA and an .885 save percentage.
The 21-year-old Brossoit had been assigned to the Bakersfield Condors of the ECHL after the Oilers franchise acquired him from the Calgary Flames in a trade on Nov. 8. He had been promoted to the American Hockey League's Oklahoma City Barons before the recall to Edmonton.
Brossoit has a 2.20 GAA, a .920 save percentage and a 19-9-2 record with Bakersfield. He went 2-0-0 with the Alaska Aces prior to the trade. He leads the ECHL in shutouts with seven.
Brossoit has played eight games with Oklahoma City this season, posting a 3.60 GAA and .888 save percentage.