An Iraqi official speaking on condition of anonymity said three civilians were also wounded and helicopters had bombarded some buildings in Sumar.
Monday's attack against the US patrol in Mosul takes to 36 the number of soldiers killed in Iraq this month, up from 23 in December.
A total of 3,940 US service personnel have been killed since the US led invasion to topple Saddam Hussein in 2003.
US commanders say Mosul, located 390km north of the Iraqi capital, is the last major hub of al-Qaeda since the group's loss of its previous strongholds in Baghdad and Anbar province.
The US military has said Iraqi security forces will take the lead in Mosul.
But Abdel Qader Jassim Mohammed, Iraq's defence minister, said the situation in Mosul is "worse than imagined" after he toured the city on Sunday.
Mohammed was critical of the Iraqi army's deployment in Mosul.
"The forces are scattered. The military units are distributed in Mosul in a way that means they haven't studied the area," he said.
On Sunday Mohammed al-Askari, a defence ministry spokesman, announced that military reinforcements, comprising troops, tanks and vehicles, had reached Mosul.
Nuri al-Maliki, the Iraqi president, promised on Friday a "decisive battle" against al-Qaeda after the Mosul blast.
The explosion took place in an unoccupied building that officials said was being used by al-Qaeda to store weapons and explosives.