The 35-year-old was playing just his second game since returning from a previous break to his left collarbone when he went down on the final play of his side's 33-14 defeat to the Panthers after being sacked.
X-rays on the bone were inconclusive after the game with more tests planned for Friday, but ESPN claims that a source has said the quarterback is done for the season as a result of the setback.
According to the report, Romo said that the injury felt similar to his first break early in the season, and added: "You can hear something happen. You are just disappointed, frustrated."
The Cowboys quarterback had recently returned after missing seven games since picking up the first injury during a week two victory over the Philadelphia Eagles.