Witness Gregory Lynthacum said the girls, from two families, fell when their basket appeared to get caught on another basket.
"It was like watching water pouring from a glass," he told WATE.com. "They bounced off the metal bridging of the ride and eventually hit the ground."
A witness said she saw blood coming from the girls' mouths and thought they were dead. Photo / AP
Mr Lynthacum said the ride only stopped after people screamed at the ride operators.
The Tennessee Bureau of Investigation will not assist police with the investigation.
Captain Tim Davis said a third-party inspector will determine "whether there was a mechanical issue" with the ride.
The Green County Fair announced on their Facebook page that all rides will be shut down "until further notice."
Tennessee Department of Labor and Workforce Development said last week there had been four amusement device accidents in the state since July 1, WATE.com reported.
We would like to extend our thoughts and prayers for those injured tonight at the fair. We are deeply shocked and...
The news comes after 10-year-old Caleb Thomas Schwab died after riding the world's tallest water slide, the 17-storey Verruckt, in Kansas over the weekend.
Witnesses said Caleb was "decapitated" after being flung from the ride.