Viggo Rohl Pastrnak was born on June 17 and died on June 23, Pastrnak announced on Instagram.
"We have an Angel watching over us and we call him SON. You will be loved FOREVER," Pastrnak wrote. "Please respect our privacy as we are going through these heartbreaking times."
He did not disclose the cause of his son's death.
"We are heartbroken by the passing of David and Rebecca's son, Viggo. David and Rebecca are a part of our family and we share in their loss. Please keep them in your thoughts and respect their privacy during this very difficult time," the Bruins said.
The 25-year-old Pastrnak, a two-time All-Star, had told NHL.com in May about his excitement at becoming a father.
"You come home and you don't think about hockey at all, you obviously have other priorities," Pastrnak told the league's website. "You're getting ready for the baby and we couldn't be more excited. So, hockey's not been talked much lately at home and sometimes that's good, you know?
"When things are going well, it's good, and when things are not going well, sometimes you just need to think about other stuff. For me it's been definitely something new, but I'm so excited. Family is always going to be No. 1. ... I'm grateful that I can live and work with a job that I love, but at the end of the day it's just a game. [My family] is always going to be No. 1."