The Flames said in a release that Emmerson Stajan died on Monday following childbirth.
"Our thoughts and prayers are with Katie and Matt at this difficult time," the Flames said in a statement. "We appreciate that everyone has and will continue to respect their privacy during this period."
Stajan signed a four-year extension with the Flames earlier this year. He has 10 goals and 13 assists in 52 games this season.
The Flames said a private memorial service will be held in the coming days.