Shero, 51, was named GM of the Penguins in May 2006. He was named the 2013 GM of the Year, led the team to back-to-back Stanley Cup Final appearances and a championship in 2009.
Bylsma, who was signed through the 2015-16 season, was named coach of the Penguins on Feb. 15, 2009.
He became the fourth-fastest coach in NHL history to reach 150 wins (251 games) on Feb. 26, 2012 vs. Columbus, and won the 2011 Jack Adams Awards as Coach of the Year.
Penguins President David Morehouse indicated that Assistant GM Jason Botterill will take over as interim GM until a new GM is hired.
"We don't have anyone in particular in mind (for the GM vacancy). We have a large group of people in mind," Morehouse said. "We think we'll have a lot of interest, but we have no one in particular that we're looking at."
Botterill will be considered for the full time position.
Once a new GM is hired -- and Morehouse indicated that may not happen before the NHL Draft in June 27-28 -- that person will determine whether or not Bylsma will return behind the bench.
It has been widely reported that Bylsma could be let go once a new GM is brought in.