Cowboys officials said after the game that Ware was "aware and alert with full movement and strength in his extremities" when he was taken off the field.
He was then taken to a local hospital for X-rays and further evaluation.
After getting hurt early in the fourth quarter of Sunday's game against San Diego, Ware was stablized on a stretcher and carted off the field.
"Initially, it looks like right at the base (of his neck), he had a sprain," Cowboys owner Jerry Jones said. "We feel very good about everything was moving, everything was going. It was just by the nature of where it was.
"The doctors felt good."
Ware signed a $78 million, six-year contract extension through the 2015 season that included a $20 million signing bonus back in October.
Dallas head coach Wade Phillips said afterwards, "We had concern for our player first, that was a big thing we were trying to get everyone organized to get back to playing the game.
"It gave them some rest time I think."
Ware's status is expected to be updated Monday.