The soldiers disobeyed orders to haul fuel to the Iraqi town of Taji, north of Baghdad, on Wednesday because their vehicles were considered unsafe, said Patricia McCook, wife of Sergeant Larry McCook.
She told the Clarion Ledger newspaper in Mississippi her husband called saying that he and the 16 other reservists were read their rights and moved from the military barracks into tents.
McCook said her husband explained to her the details of their predicament during a panicked phone call at about 5am (1000 GMT) on Thursday.
The newspaper reported the platoon could face charges of wilful disobedience of orders, which is punishable by dishonourable discharge, forfeiture of pay and may include up to five years confinement.
No official comment
No military officials have confirmed or denied the detainment of the platoon.
US soldiers have come under
dozens of attacks daily in Iraq
"I got a call from an officer in another unit early [on Thursday] morning who told me that my husband and his platoon had been arrested on a bogus charge because they refused to go on a suicide mission," said Jackie Butler, wife of Sergeant Michael Butler, a 24-year reservist.
"When my husband refuses to follow an order, it has to be something major," she told the Clarion Ledger.
Amber McClenny, 21, is among those being detained the newspaper reported.
She pleaded for help in a message left on her mother's answering machine early on Thursday morning.
"They are holding us against our will," McClenny said. "We are now prisoners."
McClenny told her mother her unit was told to re-deliver fuel to another base in Iraq on Wednesday, after their initial delivery was found to be contaminated with water. After returning to their base, they were told to take the fuel to another base, the paper reported.
The platoon is normally escorted by armed Humvees and helicopters, but did not have that support on Wednesday, according to McClenny's account to her mother.
"They are holding us against our will. We are now prisoners"
Amber McClenny, 21
The Clarion Ledger article indicated that other reports of insufficient materials and support had been coming out of Iraq.
McCook said her husband, a staff sergeant, understood well the severity of disobeying orders. But he did not feel comfortable taking his soldiers on another trip.
Kathy Harris, mother of Aaron Gordon, 20, who is among those being detained, said her primary concern is that she has been told the soldiers have not been provided access to a judge advocate general.
"US law requires that confined soldiers be given a hearing before a magistrate within seven days," the paper concluded.