Albert suffered the injury in Miami's 20-16 loss Sunday to the Detroit Lions.
"That's unfortunate with any player who sustains an injury," Philbin said. "Branden has been a great addition to the football team and an excellent representative of the organization. Unfortunately, injuries are part of the game."
Albert signed a five-year contract with the Dolphins this past offseason worth a maximum of $47 million. He started nine games for Miami and played at a high level.
Dolphins rookie first-round pick Ja'Wuan James is expected to replace Albert and move from right tackle to left tackle. Miami (5-4) will host the Buffalo Bills (5-4) Thursday night in what could be be an elimination game in a crowded AFC playoff field.