AP Television News footage showed several ambulances destroyed and on fire, thick black smoke rising from them as firefighters worked to put out the flames.
The strike, made from a ground launcher, took out a militant "command-control center," the U.S. military said. The center was located in the heart of the eight-square-mile neighborhood that is home to about 2.5 million people. Iraqi officials said at least 23 people were wounded, though none of them were patients in the hospital.
The U.S. military blamed the militants for using Iraqi civilians as human shields.
"This is a circumstance where these criminal groups are operating directly out of civilian neighborhoods," military spokeswoman Spc. Megan Burmeister told The Associated Press in an e-mail.
She said it presents a "complex and very difficult" challenge for U.S. forces to strike the militants when they are "putting themselves next to municipal buildings."
Dr. Ali Bustan al-Fartusee, director general of Baghdad's health directorate, told the AP that 23 civilians were wounded in the strike.
He said no patients in the hospital were hurt, but that some of the wounded included civilians outside on their way to visit patients in the hospital. He also said 17 ambulances were damaged or destroyed.
AP Television News footage showed about 100 people milling about in the rubble of the destroyed building. A deep crater was seen just yards from the hospital, which is surrounded by 15-foot-tall concrete blast walls. It appeared that one section of the blast wall was leveled.
Windows were blown out of cars in the hospital's parking lot, but there did not appear to be any damage to the hospital itself.
Shiite extremists are known to have operated in a building next to the hospital, local reporters said.
U.S. and Iraqi forces have waged street battles with Shiite militias since late March in Sadr City, the power base of radical Shiite cleric Muqtada al-Sadr and his Mahdi Army militia.
The fighting is part of a 5-week-old crackdown by the Iraqi government and U.S. forces on Shiite militia factions. The clashes have brought deep rifts among Iraq's Shiite majority and have pulled U.S. troops into difficult urban combat.
Militia members have been blamed for firing hundreds of rockets or mortars from Sadr City into the Green Zone, the U.S.-protected area housing the American embassy and much of the Iraqi government. In the past month, more than a dozen people - including two American civilians and soldiers - have been killed inside the zone during the attacks.
In response to the shelling, American and Iraqi troops in recent weeks have moved into Sadr City, hoping to push the militants far enough from the Green Zone so their rockets and mortars would be out of range.
Iraq's Prime Minister Nouri al-Maliki, a Shiite, shows no indication of easing the pressure on militia groups, including the powerful Mahdi Army led by al-Sadr. Al-Maliki has been seeking to increase leverage on Iran, which is accused of training and arming some Shiite militia groups. Iran denies the claims.
A five-member Iraqi delegation returned from Tehran Saturday from a meeting aimed at halting suspected Iranian aid to militiamen.
Ranking deputy Khalid al-Atiyah said the Iranian government had expressed its readiness to assist the Iraqi government" against the extremists and "in its security measures." He did not elaborate.
During clashes over the past two days in Sadr City, at least 100 people have been killed, Iraqi health officials said.
Also Saturday, the Turkish military claimed air strikes it carried out earlier this week in northern Iraq killed more than 150 Kurdish rebels. The military said it successfully hit all its targets in a three-hour air operation on Mount Qandil early Friday.
The leadership of the Kurdish rebel group is believed to be hiding in the Qandil region - about 60 miles from the Turkish border.
In northern Iraq, Ahmed Danaf, the head of external relations for Kurdish group, claimed in a phone call that the raid killed six members of the Free Life Party, the anti-Iran Kurdish group PEJAK.
The U.S. military also said Saturday that a U.S. soldier died of wounds suffered in a roadside bomb that struck the soldier's vehicle during a combat patrol in eastern Baghdad the day before.
Georgian Defense Ministry spokesman Giga Tatishvili said two servicemen from the ex-Soviet republic were killed and one wounded south of Baghdad on Friday when a parked car bomb exploded. The deaths were the first combat fatalities the nation's military has suffered in Iraq, where it has had a presence since August 2003.