Ware suffered a sprained neck and was taken to a local hospital for X-rays as a precaution. He was alert and had feeling in all his extremities. The linebacker had tissue damage but nothing structural.
"Initially, it looks like right at the base that he has a sprain," Cowboys owner Jerry Jones said. "I don't want to get into medicine. Obviously I'm not qualified, but 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. He's at the hospital right now."
Later Sunday, Ware was released from the hospital and is expected to miss two weeks, sources close to the situation told ESPNDallas.com. The Cowboys (8-5), who fell out of the NFC East lead when Philadelphia beat the Giants late Sunday, play at 13-0 New Orleans on Saturday night and visit Washington on Dec. 27.
Ware spent Sunday night icing his neck at home and had significant soreness and swelling, one source said.
Ware was rushing Chargers quarterback Philip Rivers with 11:28 to play in the fourth quarter when his head smashed into Dombrowski's left hip. Ware's wife, Taniqua, rushed down to the field with several family members.
The linebacker was moving his arms and legs before doctors and trainers came onto the field to get him.
Trainers removed Ware's face mask before lifting him onto a cart.
"The good thing is we saw him moving. Definitely from that indication, things weren't going to be too bad," said teammate Terence Newman, who spoke to Ware while he was being loaded on the cart. "But the fact you're taken off on a stretcher, you're still always nervous."
As Ware was being wheeled into the tunnel with associate trainer Britt Brown, he waved both his hands and wiggled his feet. He also gave a thumbs-up and made a motion with his fingers to look like a W.
"Nobody really wants to get hurt. We talked at one point and he was telling me to tell his [teammates] when I got in [the locker room] that he was all right," Cowboys inside linebacker Bradie James said. "But we saw him moving. Anytime that you have a neck issues, or something happens to your neck, it just really lets you know how precious life is."
Ware leads the Cowboys with nine sacks and 35 quarterback pressures coming into the game.
"We all love DeMarcus and obviously he's an incredible player," Cowboys quarterback Tony Romo said. "But more important to all of us, he's a great guy and he's a joy to be around. Rain or shine he has a smile on his face and he's always lifting everybody's spirit. We'll be praying for him."
In October, Ware agreed to a $78 million, six-year contract extension through the 2015 season that included a $20 million signing bonus. The 27-year-old Ware was in the final year of the contract he signed after being the 11th overall pick in the 2005 draft.
The Cowboys drafted Ware over Shawne Merriman, who was taken the next pick by the Chargers. The two standout defenders have been linked ever since. They keep in contact with each other, consider each other friends, and were playing in the same regular-season game for the first time.
"I told him I'd call and check up on him," Merriman said. "It sounds like he's in good shape. I think it was just precautionary."
Ware was replaced by Victor Butler.
ESPNDallas.com's Tim MacMahon and The Associated Press contributed to this story.