The news is a major blow to the defensive corps, which likely will be without captain Chris Pronger, lost Matt Carle via free agency to the Tampa Bay Lightning this offseason and failed to sign either Ryan Suter or Shea Weber.
Holmgren said there was no timetable for how long Meszaros will be sidelined.
"We'll have a better idea after six weeks and once we see how things are progressing," Holmgren said.
Though there are other options available with restricted free agent defenders P.K. Subban, Michael Del Zotto and John Carlson on the board, it appears as though Holmgren will find solutions on defense from within the organization.
As it stands now, youngsters Erik Gustafsson, Marc-Andre Bourdon, Brandon Manning and recently acquired Bruno Gervais might be looked to as possible short-term solutions. Bourdon played 45 games with the Flyers and Gustafsson appeared in 30 contests during the 2011-12 season. Manning saw action in four games. Gervais signed a two-year contract with the Flyers this offsesason.
"We've got a lot of young kids we like," Holmgren said. "Marc-Andre Bourdon played a lot of games for us last year. Gustafsson played a fair amount and Brandon Manning got his feet wet. We have some kids that we like, and we have four guys with a lot of experience as well."
The four experienced members are Kimmo Timonen, Braydon Coburn, Luke Schenn and Nicklas Grossmann, who become Philadelphia's top four along the blue line. Bruno Gervais and Andreas Lilja would likely be a third defensive pairing.
Meszaros was traded by the Lightning to the Flyers in July 2010 in exchange for a second-round pick last June. In 143 games with the Flyers spanning two seasons, Meszaros has 15 goals and 57 points. He had seven goals and 25 points in 62 games last season.