"It looks like he's out for the year," Jones said on KRLD-FM on Tuesday morning.
A source told ESPNDallas.com that Waters wants to attempt to play through the injury but that team officials are telling him he needs his triceps repaired.
Waters suffered injuries to his ribs, knee and triceps in Sunday's loss to the Detroit Lions.
"Just trying to make it out of Detroit alive, man," Waters said Sunday.
When asked on Monday if he made it, Waters joked, "Yeah."
This is a major blow to the Cowboys' offensive line. Dallas tried to improve the interior by signing Waters prior to the start of the season.
Waters replaced Mackenzy Bernadeau in the starting lineup and was credited with helping the younger players on the line -- rookie center Travis Frederick and second-year guard Ronald Leary -- improve their respective games.
"He's done a lot," Cowboys coach Jason Garrett said Monday. "Maybe as much as anything else, it's his demeanor. He's a guy that plays the game the right way. He's physical, he's tough, he knows what to do, he plays with a little bit of an edge to him -- and that's a positive thing. I've talked to our team about it -- it's contagious."
When the Cowboys place Waters on injured reserve, it will allow them to officially sign defensive end Everette Brown to the active roster.
Brown worked out for the Cowboys on Monday afternoon at Valley Ranch.