DETROIT, July 13 (Reuters) - Volkswagen AG (VOWG_p.DE) said on Tuesday it shut down production at its Chattanooga, Tennessee, assembly plant due to a fire, but is scheduled to resume work there on Wednesday. Some employees were treated for smoke inhalation but no one was seriously injured by the fire, which was extinguished shortly after 9 am ET, a spokesman said. The cause of the fire is under investigation. VW builds the Passat sedan, and Atlas and Atlas Cross Sport SUVs at the plant, which employs about 3,800 people. The spokesman did not disclose how much volume was lost due to the shutdown.