Hiller reportedly had minor surgery after experiencing the attack working out in Switzerland.
"The procedure nowadays ... they can do it arthroscopically," Flames general manager Brad Treliving told the Calgary Herald on Thursday. "They’re saying within nine to 12 days you're up and back to normal.
GAA: 2.48 | SVP: 0.911
Hiller signed with the Flames on July 1 as a free agent. His two-year contract reportedly is worth $9 million.
Hiller, 32, was 29-13-7 with a 2.48 goals-against average and .911 save percentage in 50 regular-season games for the Anaheim Ducks in 2013-14, but he lost his starting job during the Stanley Cup Playoffs.
He was benched in favor of Frederik Andersen to start the playoffs against the Dallas Stars, and after briefly regaining the No. 1 spot because of an injury to Andersen, the Ducks turned to John Gibson during the second round against the Los Angeles Kings. The Ducks lost the series in seven games.
Hiller won at least 26 games in each of the past four full seasons for the Ducks.