An "unknown type of explosive device" hit the convoy at about around 2145 local time (1845 GMT) on Wednesday.
The three soldiers were taken to a military hospital where one died just over an hour later of his wounds.
Of the surviving casualties, one was said to be in serious condition and the other stable.
Based on the latest Pentagon figures, the death brings to 1065 the number of US troops killed in Iraq since last year's invasion.
Falluja, 50km west of the Iraqi capital, has become a no-go area for foreign ground troops, but it is a regular target for US warplanes.