With third-choice keeper Carl Ikeme also injured, Wolves boss Mick McCarthy has moved quickly to take Stake to Molineux to provide cover.
Stack - who played for the Republic of Ireland U-21 side when McCarthy was in charge of the senior Ireland team - has started just one league game for the Royals since moving from Arsenal in 2005, and spent much of last season on loan at Leeds United.
"Graham's an experienced keeper who I had no hesitation in taking. He'll be on the bench on Saturday," McCarthy said.
"He lost his slot at Reading through injury, but he doesn't want to just sit there and pick up his money, he's going to come here and compete for a place."