Coach Wade Phillips said Barber had an MRI on Monday, a day after he was hurt on a 35-yard run in the fourth quarter of the Cowboys' 33-31 loss to the Giants.
"We don't know exactly where he is," Phillips said. "Other than that, I think we came out fairly well injury-wise."
Barber gingerly walked off the field after his final run in the home opener. The hard-running Barber appeared to stumble on his own just before getting tackled at the 7, setting up Felix Jones' touchdown run the next play.
Barber had 18 carries for 124 yards with a 2-yard touchdown, the first scored in the new Cowboys Stadium. Jones finished with 96 yards rushing and Dallas had 251, its most since 1993.
The Cowboys host Carolina next Monday.