The dam gave way just before 1 a.m., burying a road and railway tracks leading to the plant under a thick layer of dark-grey mud and water.
Authorities said no one was seriously injured or hospitalized.
Investigators were trying to determine exactly what caused the breach, but the TVA spokesman said heavy rains and freezing temperatures may be to blame.
"I am still in shock," said Crystell Flinn, 49, whose ranch-style house was pushed off its foundations and driven some 10 metres onto a road. "I don't think it really has hit me yet."
Flinn was travelling back from Knoxville when a friend called her cellphone to say she heard that the flood hit Flinn's house and that her 53-year-old husband, James Schean, was trapped inside. Schean escaped cold and shaken but not injured.
Knoxville-based TVA supplies electricity to 8.8 million consumers in Tennessee, Mississippi, Alabama, Kentucky, Georgia, North Carolina and Virginia.