Dr. James Andrews will repair labrum tears both players have in their left shoulder. Recovery time is expected to be within six months.
Ranger has played the majority of the season with his injury. Meszaros was hurt in a game against Pittsburgh on Feb. 4.
"We feel it is important to get the shoulders repaired so they can be fully recovered and ready to go at the start of training camp for the 2009-10 season," Tampa Bay general manager Brian Lawton said in a statement.
The Lightning started Thursday 13th in the Eastern Conference and will likely miss the playoffs for the second straight season.