Moorman was injured while warming up before Wednesday's practice and won't play Sunday at Baltimore.
"Freak deal, not much I can do about it," Moorman said after Thursday's practice. "It's frustrating, just want to get it healthy and see where it takes me."
The Cowboys have two punters on the active roster, only because of Jones' injury. Now with Moorman nicked up, it places pressure on Jones to return.
Coach Jason Garrett said the front office has scanned the waiver wire seeking a punter.
Highland Park’s Daniel Sepulveda, Chas Henry, who was cut earlier this season by Philadelphia, and T.J. Conley will punt for the Cowboys. Sepulveda had his career in Pittsburgh cut short because of five knee surgeries but has a 43.7-yard average for his career.
Moorman, who was cut by the Buffalo Bills before signing with the Cowboys, had three punts for 111 yards in the Week 4 loss to the Chicago Bears. Moorman sent two punts inside the 20 and finished with a net average of 34.3 yards.
"It's frustrating as far as the timing goes," Moorman said of the injury. "Not for me but for the team. I put them in a difficult spot. I'm an internal optimist. I think I can fight through it, but it's only so much you can do (with) a muscle strain."