Ian Rapoport of NFL Network first reported the news, noting the injury is expected to keep the starter out six to eight weeks. Cowboys COO Stephen Jones confirmed the surgery in an interview with 105.3 The Fan's K&C Masterpiece.
Michael Gehlken of the Dallas Morning News added Vander Esch will be placed on injured reserve with a designation to return.
Vander Esch plays a significant role for the Cowboys when healthy, earning a Pro Bowl selection as a rookie in 2018 after leading the team with 140 tackles. He added 72 tackles in just nine games last year until a neck injury forced him to injured reserve.
The Idaho State product had offseason neck surgery and was set to enter this season at full strength before his comeback was cut short by another injury.
The 6'4", 256-pound middle linebacker could seek a contract extension in the offseason, but injuries will likely remain a concern for the Cowboys.
With Sean Lee already on injured reserve, the Cowboys are now especially thin at linebacker alongside Jaylon Smith. Joe Thomas filled in for Vander Esch against the Rams and will likely have a significant role going forward after finishing with five tackles and a quarterback hit.
"We have depth," Smith said after the game, per Todd Archer of ESPN. "Joe stepped in and did a good job making plays. I just think collectively as a defense, myself included, we've all got to play better. We have a standard and we have to play up to that."
Thomas, 29, appeared in 15 games last season, starting two, while totaling 33 tackles. Justin March can also see more playing time on defense, while Francis Bernard could be promoted from the practice squad.