Woodruff and his cameraman, Doug Vogt, were flown from Iraq on Sunday.
Doctors at the Landstuhl Regional Medical Center roused Woodruff briefly from sedation, ABC reported. He responded to stimuli to his hands and feet.
The two men are expected to be flown to the United States for more treatment, possibly as soon as Tuesday.
"It's gonna be a long road, but he's a strong guy, and he's gonna make it, and he's gonna do well," said Woodruff's brother, Dave. "And I think the care he's gotten has been just world class so far. So with that, we can feel pretty good about him."
Woodruff, 44, and Vogt, 46, were wounded in a roadside bombing and sniper attack Sunday near Taji, about 20 miles north of Baghdad.
Both suffered head injuries. Woodruff also suffered wounds to his upper body and broken bones, ABC said.
The network said the men were wearing helmets and body armor.