Wall, 21, has played most of the season with Portland of the AHL, posting a 10-6-1 record with a 3.13 goals-against average.
But the acquisition of Wall makes for a logjam of goalies for Colorado, which already has Peter Budaj and Jose Theodore.
May has missed 53 games this season after shoulder surgery on Sept. 28. He was injured in a preseason game against Detroit and then played in 10 contests for Colorado, notching three assists.
"Michael Wall is a solid prospect who will help the goaltending depth in our system," Avalanche general manager Francois Giguere said.
Wall has been recalled by the Ducks two times this season, going 2-2 with a 2.97 GAA.
Parker was traded by Colorado to the Sharks in June 2003 for a fifth-round draft pick. He's played in only 11 games this season due to ankle and back injuries.
The Avalanche players were in a jovial mood before the trade deadline, even joking about who may be dealt.
"You've got to laugh about it," forward Ian Laperriere said. "I asked the guys for their tickets for (Tuesday night's) game if they get traded.
"It's on everyone's mind, unless you're Joe (Sakic). He knows he's not going anywhere."
Colorado also announced Tuesday that defenseman Karlis Skrastins will be out for up to 10 days with a sprained knee. The Avalanche recalled defenseman Kyle Cumiskey from AHL Albany to take Skrastins' place.
Skrastins's streak of 495 consecutive games ended when he couldn't play Sunday night against Anaheim. It was the longest run by a defenseman in NHL history.
Skrastins injured the knee the night before in a 6-5 shootout loss to the Los Angeles Kings.
"We'll miss him certainly," Colorado coach Joel Quenneville said. "You've got to commend him on an outstanding streak and how competitive he is."
And while Colorado is currently in 10th place in the Western Conference -- 12 points behind Calgary for the last playoff spot -- they're still holding out hope for the postseason. The Avalanche have made the playoffs every season since moving to Denver in 1995.
"It looks bleak. But there's still a chance," Brunette said.