The incident took place in a remote area between Uppar Anchal Bari and Hataguma when the tractor, carrying about 60 persons from Hiranpadu village, plunged into gorge after one of its front wheels broke on a hill top.
The victims, including women and children, were returning home at Hiranpadu village after attending a wedding at Seriguma village when the accident occurred, Rayagada SP Rajesh Pandit said.
"So far, we have information regarding death of 20 persons but the bodies are yet to be identified," said Tapan Mohanty, inspector in-charge of Rayagada Police Station.
Chief Minister Naveen Patnaik announced medical expenses of the injured would be given from Chief Minister's Relief Fund and State Treatment Fund.
He directed the district collector of Rayagada to shift seriously injured persons to a nearby hospital at Vishakhapatnam in Andhra Pradesh.
"The district administration has decided to refer three of them to a hospital at Vishakhapatnam," said Sashi Bhusan Padhi, Rayagada district collector.