Major-General Tarik al-Baldawi, an officer at the Iraqi Interior Ministry, survived an assassination attempt on Tuesday when fighters armed with machine guns attacked his convoy in al-Adil neighbourhood, west of Baghdad, Aljazeera reported quoting an Interior Ministry official.
The attack took place while the US defence secretary was visiting Baghdad.
Donald Rumsfeld arrived in the Iraqi capital on Tuesday morning for his second visit in three months.
The three injured included al-Baldawi's son, according to the official.
In a separate attack in the northern city of Mosul, a car bomb targeting a US convoy killed at least five Iraqis and wounded three others on Tuesday, police and hospital officials said.
A second car bomb targeted another US convoy near Mosul, hours after the first.
There was no immediate word on casualties.