Smyth was hurt during Colorado's 4-3 overtime loss at Phoenix on Monday. The club said Thursday the fracture was discovered during a follow-up MRI.
Smyth has 28 points, third-best on the team, with 11 goals and 17 assists in 36 games.
Head trainer Matthew Sokolowski said Smyth is expected to make a full recovery.
Sakic, who underwent successful hernia surgery Dec. 28, is expected to be out eight to 12 weeks.
"Arnie has been skating and progressing well," Avalanche coach Joel Quenneville said before Wednesday's 5-2 loss to Phoenix.
Colorado recently recalled rookie T.J. Hensick from AHL Lake Erie to add some offensive punch. It's his second stint with the Avalanche this season. He has one goal and two assists in 12 games with Colorado.
"I'm glad to be back," Hensick said. "If I play at a consistent level, I can play in this league."
Quenneville is hoping Hensick can ease the loss of Smyth.
"He's a guy who can help us," Quenneville said.
The Avalanche are in the midst of a four-game losing streak, including three at home. The team had been virtually unbeatable at Pepsi Center earlier in the season.
Colorado forward Ian Laperriere said Wednesday it will be a challenge to make up for the losses of Smyth and Sakic.
"You need more than one [person] to step up to fill the void," Laperriere said. "It takes a team effort."