Emerson Stajan died March 3 following his birth.
Stajan is currently on leave from the Flames.
"We would like to take this opportunity to thank everyone for the incredible outpouring of love and support, during this very difficult time," the Stajans said in a statement released by the Flames on Monday. "All of you have touched our lives with your kindness and compassion, and we truly appreciate everyone's thoughts and prayers.
"Our son, Emerson, will forever be in all of our hearts. Thank you for taking the time to think of us, and grieve this unbearable loss with us. It means so much, and we are grateful for all of your support."
Stajan signed a four-year extension with the Flames earlier this year. He has 10 goals and 13 assists in 52 games this season.