A spokesman said 15 soldiers have been injured but could not confirm whether it was a deliberate attack, nor could he comment on the nationality of the truck driver.
The white pick-up truck had driven into a line of personnel lining up outside a military shop known as the "PX" at the Udairi Camp.
Eyewitnesses said shooting then broke out, and an ambulance was called in. Egyptian immigrants who were working at the base were reportedly taken outside and forced to the ground before being questioned.
The commander of the US-led forces in Iraq, General Tommy Franks, told a news conference in Qatar that an investigation was being carried out into the incident.
Udairi Camp is a springboard for operations in Iraq.
According to the BBC correspondent Allan Little in Kuwait security is tight at the base making it virtually impossible for an unauthorised driver to enter.
An apparent suicide attack against US forces near Najaf in southern Iraq left four soldiers dead on Saturday.
Iraqi Vice-President Taha Yassin Ramadan declared that the attack marked the start of the "routine" use of suicide bombing to fend off coalition troops.
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