"Two to five houses were destroyed. Among the wounded are several women," he said.
The US said its soldiers, accompanied by Iraqi special operations troops, directed aircraft to fire on two buildings where armed men were hiding.
"The targeted Shia extremists are part of a terrorist cell," the US military said in a statement.
The statement said the armed group was "responsible for attacking local police and conducting illegal checkpoints to intimidate, extort and murder local citizens".
It also said the group "conducts extra-judicial killings of Sunnis".
Reuters television footage showed at least 11 buildings had caved in or had been levelled in three adjoining streets in the densely packed neighbourhood.
An official at Muqtada al-Sadr's, the Shia leader who commands the al-Mahdi Army, office in Washash, who declined to be named, said: "This is a catastrophe. We have pulled 24 bodies from the rubble."
Residents said the aerial bombing was preceded by clashes between US soldiers and armed groups.
The US military has launched a series of operations, including air attacks, against what it calls rogue elements of the al-Mahdi Army.
It says many of these "rouge elements" have links to Iran, which it says is supplying weapons and training to the army, a charge Tehran denies.
Last week al-Sadr ordered the group to suspend its operations for six months.