Martin will undergo surgery and will be out of action for approximately six weeks.
The Stanley Cup Playoffs are begin in 4-1/2 weeks.
Deryk Engelland regained his spot in the lineup, replacing Martin against the New York Islanders on Saturday afternoon. The Penguins also are without Kris Letang, the NHL's leading scorer among defensemen, for at least a week because of a lower-body injury.
Martin ranks ninth in the NHL in defenseman scoring with 21 points (six goals, 15 assists). He has rebounded nicely from what he has openly called a poor season in 2011-12 and had become a valuable two-way presence logging 25:22 of ice time per game.
Martin spent much of the season paired with Brooks Orpik, as well as often playing the point on the Pittsburgh power play that ranks third in the League. Only Orpik averages more time per game on the penalty kill among the Penguins.
Bylsma said Matt Niskanen would be paired with Orpik going forward. Against the Islanders, Bylsma said the plan was for Mark Eaton to play alongside newly acquired Douglas Murray and for Engelland to partner with rookie Simon Despres.
"That will kind of be the way it looks," Bylsma said. "But also ... there will be some rotating in terms of responsibilities over the next three, four, five games."
The Penguins (27-8-0) have won 14 consecutive games and entered Saturday leading the Eastern Conference standings by seven points over the Montreal Canadiens. The League record is 17 straight wins, set by Pittsburgh 20 years ago.
Martin is in the third season of a five-year, $25 million contract.
Pittsburgh acquired Iginla, Murray and forward Brenden Morrow earlier this week. Murray's arrival made Engelland a healthy scratch Thursday for the third time this season.