The duo said in a statement that the FBI were currently searching for their driver, who was last seen on September 26 in Los Angeles.
The band have lost their luggage, which was on the bus, as a result of the disappearance.
Guitarist/singer Alison Mosshart said: “It is thought that the driver has committed grand theft auto or that he is in some kind of trouble.
“The bus and driver were last seen on the morning of September 26 at a Prevost dealership in Los Angeles. The driver got some new tyres and was set to head to Austin, Texas to meet up with us. His phone has been off since that afternoon.
Federal investigators and police are searching for the bus and driver throughout the US and Mexico. We are currently travelling to Nashville and have no luggage or belongings.”
Despite the disappearance of the van, Mosshart said the band were remaining upbeat.
“Aside from this bad luck,” she said, “touring with The Raconteurs has been great, so we’re in good spirits. The magnitude of the loss hasn’t quite sunk in to our shell-shocked bones.”
Mosshart added that anyone who sees a black Prevost tour bus with “Tennessee plates 0305 EA” should call the US police.