Brig. Gen. Jeffrey Dorko was in stable condition and was evacuated to Landstuhl Regional Medical Center in Germany. His injuries were not life-threatening.
A second soldier wounded in the attack was treated and released.
Dorko is commanding general of the Gulf Region Division.
In other violence Monday, a suicide bomber on a bicycle blew himself up in a crowd of police recruits in Baqouba, killing at least 29 people, police and hospital officials said. At least 19 people were wounded in the attack.
The recruits were waiting to be allowed inside the camp for the day's training when the suicide bomber blew himself up in their midst, according to a police officer who spoke on condition of anonymity because he was not authorized to speak to the media.
The attack bore the hallmarks of al Qaeda in Iraq, whose militants have repeatedly targeted police and army recruits to discourage Iraqis from joining the country's nascent security forces.
Mohammed al-Kirrawi, a doctor at the Baqouba general hospital, said most of the victims were struck by iron balls packed with the explosives to achieve maximum casualties. He said the hospital lacked the necessary equipment to save many of the wounded.
"Among the wounded, there are seven in critical conditions and there is little hope that they will survive," he said.
Baqouba, 35 miles northeast of Baghdad, is the capital of Diyala province, where hundreds of Sunni Arab tribesmen and insurgents have in recent months joined the U.S. and Iraqi forces in the fight against al Qaeda.
A 22-year-old Sunni man from Baqouba's central Tahrir area said he was among a group of some 60 recruits when the blast struck.
Akram Salman said it must have been an inside job because the suicide bomber apparently was able to penetrate heavy security surrounding the police camp without being searched.
He said police failed to stop the bomber when he changed course suddenly from the main road toward the recruits.
"The police are infiltrated. Many people join the police but they have affiliations with al Qaeda. These infiltrators made it easy for the bomber to attack us," he said. "There are two main checkpoints on the main road leading to the camp, it would be impossible for a man on a bicycle to pass without being properly searched."
"Al Qaeda has threatened us before and prevented us from joining the police," he said. "They slaughtered many policemen, burned their houses, killed their families and blew up their headquarters. Now, when the people have defeated al Qaeda and cooperated with the government, al Qaeda staged this operation to show their presence and to give a message that they are still in control."
In other developments:
In southern Iraq, meanwhile, the U.S. military turned over security responsibilities to Iraqi authorities in the mainly Shiite province of Karbala, the eighth of the nation's 18 provinces to revert to Iraqi control.
Prime Minister Nouri al-Maliki said the southern province of Basra's security file would be transferred to the Iraqis in mid-December. The British-led forces overseeing the area already have begun drawing down and pulled back from the center of the provincial capital to the airport on the outskirts.
"This is the proof of the strong will and resolve of the good citizens of this nation," al-Maliki said at the handover ceremony in Karbala, 50 miles south of Baghdad. "The reconstruction of Iraq does not hinge on security alone, but security is the key to everything."
A new commander, Maj. Gen. Mark Hertling of the 1st Armored Division, assumed control of U.S. forces in northern Iraq on Sunday, acknowledging that violence remains high in the area but expressing confidence that the military has al Qaeda on the run. "The levels are still high in some of the northern provinces," he said. "But while they're still high ... they have been decreasing significantly."