Surrey Police, who were alerted to the closure at about 17:30 GMT, said the tunnel was expected to be closed for "at least another five hours".
Officers have been deployed to help with traffic control and co-ordinate road closures and diversions.
The tunnel diverts traffic on the A3 London to Portsmouth road at the Devil's Punch Bowl.
A Surrey Police spokeswoman urged motorists to avoid the area if possible. A diversion is in place.
The engineers behind the Â£371m tunnel, which opened in 2011, said at 1.25 miles (1.8km), it was the "longest under land" road tunnel in the UK.
Its construction followed decades of severe congestion on the A3.
The Hindhead Tunnel has been closed in both directions owing to what police believe is a "technical fault".