Police found the starving refugees as they swam half a mile into a village after their engine-less boat ran aground in the Andaman Sea last Saturday, said Superintendent S.B.S. Tyagi.
Twenty-eight of them were taken to hospital as they were found to be emaciated and very weak, Tyagi told The Associated Press.
He said the 91 refugees had set out from Bangladesh for Malaysia by way of Thailand on Jan. 2 to find jobs after paying money to traffickers.
They told Indian police that the Thai navy caught them on Jan. 13 and kept them in an isolated place for five days for illegally entering Thai waters.
Then naval officers towed them out to sea and left them adrift in the engine-less boat on Jan. 19 after giving them some rice, drinking water and cooking utensils, Tyagi quoted them as saying.
Their boat drifted for several days in the sea without any food and water before they arrived at the Indian territory around two weeks later, he said. None of them had travel documents.
On Friday, Thai government spokesman Panitan Wattanayagorn said it was unlikely that the Rohingya refugees were pushed out into the sea by the Thai Navy, but said the government would look into the matter.
"The normal practice is to prosecute refugees who illegally enter Thai waters and then deport them via land transportation," said the spokesman in Bangkok, the Thai capital.
"Normally the navy officers try to keep the refugees out of Thai waters unless they need help. Their destination is Malaysia, not Thailand," Panitan told the AP in a telephone interview.
All 91 refugees were taken to Port Blair, the capital of the Andaman and Nicobar Islands, from where they will be repatriated to Bangladesh, Indian police officer Tyagi said.
Thousands of Bangladeshis try to reach other countries each year in search of better jobs, often paying up to $300 to trafficking syndicates. They are sometimes joined by Myanmar refugees, mostly Muslims known as Rohingyas, who have fled to Bangladesh from military-ruled Myanmar.
The Rohingya number about 800,000 in Myanmar, but are not recognized as a distinct ethnicity. Rights groups say they face persecution by the military junta.
AP correspondent Thanyarat Doksone in Bangkok contributed to this report.