It is feared that many of the missing might have drowned.
'Internal security threat'
Eight policemen managed to swim ashore and were taken to hospital, the police said.
No bodies have yet been found, although rescue officials recovered some police caps.
Officials said helicopters have been sent to the area to search for any police who may have survived in the 40-metre (130-feet) deep reservoir.
Witnesses, however, said police had little hope of finding many survivors.
The Greyhound force is a special unit based in neighbouring Andhra Pradesh, long considered a safe haven for the Maoists.
It was in the area on a joint operation with the special operations group of the Orissa police to flush out the rebels from the forests.
Mineral-rich Orissa is also one of India's poorest states.
Last year, 834 people were killed in Maoist-related violence across India.
Manmohan Singh, Indian prime minister, has described the Maoist uprising as the biggest internal security threat the country faces.