The storm hit while 27 players were going through workouts. There were about 70 people in the facility, counting coaches, other team personnel and media, officials said.
Ten of the injured were taken by emergency vehicles. Two others went to hospitals on their own.
Much of the frightening scene was captured by videographers taping the practice, reports CBS News correspondent Karen Brown. (See video from CBS Station KTVT in Dallas blelow.)
The rookie minicamp going on inside was first interrupted when high winds shook the building. Lights on the ceiling swayed and flickered and the building's canopy started billowing. At first it didn't seem serious.
"People were laughing when some of the lights went out," said Steve Lansdale of Ranch Report Magazine, who was covering the practice when the roof fell. "And then all of a sudden two walls started to buckle in and people screamed and people started swearing. … I put my head down and ran for the door, and the metal door in front of me bent in half."
"It was a mad dash for the exit and for a few minutes and it was pretty foggy for me," said Dallas Morning News reporter Tim McMahon.
The condition of the injured was not immediately known but at least two were considered serious.
"This worked out very, very well from a medical point of view," said Dr. Paul Pepe, head of emergency medical services for Dallas County. "Right now, I think we don't have anybody who is in a life-threatening situation."
The white, tent-like building is large enough to be seen from miles away. It was built in 2003, for Bill Parcells' first season as coach.
Storms often make loud noises inside the so-called bubble, but this time overhead lights swayed violently. One of the team's video staff was the first out the door, followed by Nick Eatman of DallasCowboys.com. Eatman was hit by something and went down a few feet away, then heard someone screaming for help. He recognized it was Todd Archer of The Dallas Morning News.
Eatman and colleague Josh Ellis tried freeing Archer but the structure wouldn't budge. "It was like a car," Eatman said. Then safety DeAngelo Smith and linebacker Brandon Williams were able to get it up just enough for Archer to squirm out.
"All I saw was blue jerseys," said Archer, whose right elbow and legs were scraped. "I was trapped, I couldn't move. Then those guys lifted it up - not very far, but I was able to move from my side to my back. ... Once I got out of there, I looked back and the whole thing was down."
Archer said that as he fled for shelter, other players appeared to be stepping through the debris looking for others in need of help.
Eatman said one of the swaying lights wound up more than two football fields away. The giant blue star atop the building lay crumpled on the ground. The storm knocked out power at team headquarters and splintered trees across the property.
Larry Rodriguez, a local television cameraman who was in the news several years ago after he was attacked by Kenny Rogers while filming the former Texas Rangers pitcher, was treated with six stitches for a cut on a hand.
"We checked and we can't find any other damage than this particular location," said David Tull, an Irving police spokesman. "The nearby area didn't have any reports of structural damage."
Names and details of their injuries were not released due to privacy issues. DeCamillis was seen being removed on a stretcher wearing a neck brace.
"I saw it coming down and didn't have time to react," secondary coach Dave Campo said. "I hit the ground and was able to get back up."
The storm was producing winds measured at 64 mph just before it struck the Cowboys facility, said National Weather Service meteorologist Joe Harris in Fort Worth. A weak tornado is in the range of 65-110 mph, according to NWS guidelines. Power was knocked out for less than an hour.
"We're lucky no one got electrocuted with all the water in the building," head coach Wade Phillips said. "A couple of players had minor injuries, but they were all right."
This was the second of three scheduled days of practices, but Sunday's session has been canceled.
"Everybody's lucky that it wasn't worse. Cause based on that pile of wreckage out there, it could've been worse," Lansdale said.