Both journalists suffered head injuries, and Woodruff also has broken bones. They were in stable condition following surgery at a U.S. military hospital in Iraq, and due to be evacuated to medical facilities in Germany, probably overnight, said ABC News President David Westin.
"We take this as good news, but the next few days will be critical," Westin said.
Woodruff and Doug Vogt, an award-winning cameraman, were embedded with the 4th Infantry Division and traveling in a convoy with U.S. and Iraqi troops near Taji, about 12 miles north of Baghdad.
They were wearing body armor and helmets but were standing up in the hatch of the mechanized vehicle when the device exploded, exposing them to shrapnel. An Iraqi solder was also hurt in the explosion.
ABC said the men were in the Iraqi vehicle — considered less secure than U.S. military equipment — to get the perspective of the Iraqi military. They were aware the Iraqi forces are the frequent targets of insurgent attacks, the network said.
"If you're going to cover the Iraqi military, you have to go with them, you have to see how they live," said ABC News correspondent Martha Raddatz, reporting on the attack on ABC's "This Week" Sunday.
The U.S. military confirmed that Woodruff and Vogt were injured in the midday attack and said an investigation is under way.
CBS News correspondent Lara Logan, who has covered Iraq, said the Taji area is considered particularly dangerous because it was the site of one of Saddam Hussein's munitions dumps. Many of the explosives are believed to have gotten into the hands of insurgents, she said.
"I admire Bob for going with the Iraqis," said Logan, who was blown 12 feet in the air by an explosion while with the U.S. military in Afghanistan in 2003. "It's important to hear their story and to experience it from their point of view. He did the right thing."
Improvised explosives are the simplest and deadliest weapon in the insurgents' arsenal, reports CBS News correspondent Elizabeth Palmer. Made of old artillery shells or stolen explosives and hidden on the roadside, they can be triggered by anything from trip wires to cell phones.
This year, the U.S. military will spend $3.5 billion to protect soldiers with better training, and technology like robots that can find improvised explosives and detonate them, Palmer reports. But by the end of last year, improvised explosives were killing two out of every three American soldiers who died in combat in Iraq.