According to Al-Alam Al-Maqawim Network, the American convoys were targeted in the cities of Hillah and Jableh and the Al-Nile region on Wednesday.
The Qasim Al-Jabarin group has claimed responsibility for all three attacks.
No further details have been released.
Similar attacks against US troops in Iraq have been increasing in the past months.
Anti-US sentiments have been running high in Iraq since Washington assassinated top Iranian commander Ghasem Soleimani and the second-in-command of the Iraqi popular mobilization units, Abu Mahdi al-Muhandis, in January last year.
Following the attack, Iraqi lawmakers unanimously approved a bill on January 5, demanding the withdrawal of all foreign troops.