Both players were placed on injured reserve.
The Flames said Monahan's status is week to week. The team also announced Thursday that Wideman broke his left hand in Wednesday night's 3-2 loss to the Chicago Blackhawks. He will undergo surgery to have a pin placed in the hand, according to general manager Jay Feaster.
Calgary (8-12-4) plays at Anaheim on Friday and Los Angeles on Sunday.
With nine goals and six assists, the 19-year-old Monahan ranks second in scoring among NHL rookies behind Thomas Hertl of the San Jose Sharks. Monahan is also second on the Flames in points.
He took a shot off his foot in practice Nov. 21, but played in Calgary's next two games. Monahan scored his ninth goal of the season against the Blackhawks, but his foot continued to be painful. A scan Thursday confirmed the fracture.
"He will be re-evaluated at the beginning of next week and we'll have a better idea exactly what the time frame will be," Feaster told reporters Thursday.
"It's certainly not good news when these things happen. To lose a guy like Wideman, that's a tough blow for the team. Obviously with Monny, the way Monny's been playing, it's a tough guy to take out of your lineup."
The Flames have been hit hard by injuries this season. Top defenseman Mark Giordano hasn't played since he broke his ankle during a game Oct. 21. He has started skating again and Feaster is hopeful the captain will be ready to play next week.
Curtis Glencross is out two to three weeks with a knee injury and fellow forward T.J. Galiardi is day to day with back spasms.
"We've lost some significant players for a significant period of time," Feaster said. "It's important they don't become an excuse. They're not a crutch, no pun intended, to lean on.
"You try and find a way to soldier on. We have to find ways to win games with the guys we do have."
The Flames have called up forward Max Reinhart and center Paul Byron from Abbotsford of the American Hockey League.