The 18-year-old forward has a shoulder injury that requires treatment and possibly surgery, so Bennett is a non-roster injured player.
"He's probably been dealing with this for longer than he wanted to let on," Flames general manager Brad Treliving said Tuesday.
"We are going to spend the next 24 to 48 hours finalizing his plan of care. There is a strong possibility this could require a surgical procedure. We're just not there yet in terms of the final prognosis."
Calgary opens the 2014-'15 regular season Wednesday at home against the Vancouver Canucks.
The Flames drafted Bennett fourth overall in this year's NHL draft, making him the highest selection in Calgary's history.
He was limited to three pre-season games and missed parts of main camp because of a groin injury coming out of rookie camp, which was followed by his shoulder troubles.
"I had problems with this shoulder last year," Bennett said. "I didn't think anything of it. I played through it all year. It started to act up a little bit at the start of camp this year.
"Right now we're still trying to figure it out. It's really sore. We're getting some tests done. It's looking like it could be something a little more serious, but we're not 100 per cent sure what it is."
When Bennett did get into games, he demonstrated the offensive flare that made him a high draft pick. He put seven shots on net and had an assist in his first pre-season game against Vancouver.
From behind the net, Bennett set up Josh Jooris for a one-timer and Calgary's fourth goal in the team's last pre-season game at home.
But the six-foot-one 180-pounder from Holland Landing, Ont., didn't travel with the Flames to Winnipeg this past Saturday for their final exhibition game.
"Ultimately, it's a speed bump," Treliving said. "This is going to be a really good young player.
"This is a hard league. It's a hard league for young players to get into, so I don't look at this as a major setback for Sam. He's going to be back up and going."
Bennett's entry-level contract kicks in when he plays his 10th NHL game. The Flames could keep him for up to nine games and then send him back to the Ontario Hockey League's Kingston Frontenacs.
Bennett admits he kept quiet about his shoulder pain because he wanted to be in the Flames' lineup.
"I wanted to play," he said. "I'd do anything to make the team and play in the NHL this year. I didn't think it was that big a deal and it was a little bit bigger of a deal than I thought."