The mass capture came amid a surge in violence that left four US soldiers dead in less than 24 hours in attacks north of the capital, Baghdad.
The soldiers, from the Shia community in the south, were captured by armed men in Rawa, about 250km west of Baghdad, after they had left their base, said the military source, adding that nothing had been heard from them since.
The defence and interior ministries could not confirm the report.
Rawa is in the predominantly Sunni Arab Al-Anbar province that has seen several similar incidents and killings of Iraqi soldiers in the past.
In early March the bullet-riddled bodies of at least 30 members of the security forces were found on the banks of the Euphrates near al-Qaim, another border town in the restive province.
US and Iraqi officials have accused Syria of not doing enough to stop fighters crossing its border with Iraq.
Tal Afar offensive
At another flashpoint on the Iraq-Syrian frontier, a joint Iraqi-US force pressed on with an offensive against fighters in the northern town of Tal Afar, west of the main city of Mosul.
US and Iraqi forces are carrying
Four bombers were killed when their explosives-laden vehicle detonated prematurely in Tal Afar, said Captain Ahmed Amjad of the Iraqi police.
Troops have found and destroyed nine weapons caches and detained 73 suspects since the start of the operation in Tal Afar on 26 May, the US military said.
With the major offensive in Baghdad dubbed Operation Lightning in its third week, fighters appear to have shifted their focus north of the capital in a familiar pattern of moving attacks from one area of the country to another whenever they come under pressure.
At least 49 Iraqis and four US soldiers have been killed since Tuesday in attacks north of the capital.
A US soldier was killed on Wednesday when his patrol hit a roadside bomb near Ad-Dawr, a US military statement said.
In nearby Tikrit, near ousted leader Saddam Hussein’s hometown, two US soldiers were killed late on Tuesday in an “indirect fire attack,” on their base, a military statement said.
Leaflets signed by the Islamic Army group were plastered on shop fronts and walls in Tikrit claiming responsibility.
“The knights of the Ali bin Abi Taleb Brigade fired a barrage of mortars and rockets last night at the citadel of infidels in the centre of Tikrit,” said the leaflet.
Another US soldier based in Balad, also north of Baghdad, was killed in a roadside bomb on Tuesday.