Lynch, a 19-year-old Army supply clerk, arrived at a U.S. air base in southwestern Germany on a C-17 transport plane late Wednesday for treatment at a U.S. military medical center.
From Germany, she spoke with her family at their home in Palestine, W.Va. in a 15-minute telephone call.
"She's real spirited, she hasn't eaten in eight days and she's hungry," her father, Greg Lynch, said. "She wants some food."
Randy Coleman, a military spokesman in West Virginia, said she had fractures in both her legs, and her family said she also had injured her arm.
"She's weak, she knows she's injured and they're doing the best that they can to get her so she can travel," her brother Greg Lynch, Jr., said.
Her father said she will be transferred to Walter Reed Hospital in Washington "as soon as possible."
Lynch was captured by the Iraqis more than a week ago after her maintenance unit made a wrong turn and was ambushed in Nasiriyah. Twelve other members of her unit were also feared captured; five of them are officially listed as POWs.
Following an intelligence tip about Lynch's whereabouts, U.S. special operations forces made their way behind Iraqi lines and seized Lynch from the Saddam Hospital under cover of darkness late Tuesday, American officials said.
"I thought at first it was an April Fools' joke," said her father, speaking at the family's home in Palestine, W.Va. "I thought this was a cruel joke. I can put up with most things, but not that. They assured me, no, it's not a joke."
The operation also found 11 bodies — two in a hospital morgue and nine buried outside the building, said Brig. Gen. Vincent Brooks, a U.S. Central Command spokesman. He said U.S. forces were led to the graves by someone who had been taken into custody.
"We have reason to believe some of them were Americans," said Navy Capt. Frank Thorp, another Central Command spokesman.
He said the military has not confirmed whether they were members of Lynch's unit, the 507th Maintenance Company. "We don't yet know the identity of those people," Thorp said. "And forensics will determine that."
As CBS News Correspondent Lee Cowan reports, the mission to retrieve her mobilized the entire Pentagon. Virtually every asset on the battlefield was used -- from a battalion of Marines who drew fire as a decoy to U.S. Special Forces who ran through a hail of gunfire not once, but twice.
Battered and broken, Lynch finally got her wish when she was saved by strangers she still considers family. But not a single member of the secret Special Operations community will take credit for the rescue. The will only say virtually every branch of U.S. Special Forces was involved, and one calls it a midnight ballet with one tragic turn: the uncovered bodies.
"Some brave souls put their lives on the line to make this happen, loyal to a creed that they know: that they will never leave a fallen comrade," says Brooks.
The 507th was attacked March 23 during some of the earliest fighting in Nasiriyah, where Saddam's Fedayeen loyalists and other Iraqi fighters are said to have dressed as civilians and ambushed Americans.
Not long afterward, five of Lynch's fellow soldiers showed up in Iraqi television footage being asked questions by their captors.
The video also showed bodies, apparently of U.S. soldiers, leading the Pentagon to accuse Iraq of executing some POWs.
In Tuesday's raid, U.S. forces engaged in a firefight on the way into and out of the hospital but there were no coalition casualties, Brooks said. He said they found ammunition, mortars, maps and a terrain model at the hospital, along with "other things that made it very clear it was being used as a military command post."
"Some brave souls put their lives on the line to carry this out," Brooks said.
As soon as they rolled into the hospital compound, civilian patients and medical staff began emerging with their hands up. Most were allowed to leave, or to return to the building for treatment.
An Iraqi pharmacist who works at Saddam Hospital told Britain's Sky television that he treated Lynch for leg injuries but that she was otherwise healthy. But he added, "every day I saw her crying about wanting to go home."
The pharmacist, who gave his name only as Imad, said Lynch knew the U.S. troops were on the other side of the Euphrates River and "she kept wondering if the American Army were coming to save her."
As CBS News Correspondent Jane Clayson reports, just after supper Tuesday night Greg and Dee Lynch got the call at their home in Palestine, W. Va. After nine difficult days, they finally knew for sure their daughter Jessi was alive.
"I was up and down just like every day, but yesterday was going to be the day. I just knew it," says Dee.
At news of Jessi's dramatic rescue, family and close friends rushed to the Lynch home to celebrate.
"We were just so overwhelmed and happy and just hugging everyone, talking to everyone. I can't even describe it," says her friend Jenny Baileys.
And her family was saddened to hear that their daughter was injured and that she had been a POW and not just missing in action.
"We didn't know she was captive and that really hit hard," says her father. But, he says that once she is back, the town will go into full celebration with them planning "one heck of a shindig" for her.