Aid agencies warned of a humanitarian crisis after monsoons dumped rain across parts of south Asia, forcing 9.6 million people to flee their homes.
The rhinoceroses were among more than 100 animals that died when a game reserve in Assam, northeastern India, was inundated.
“Since the first week of June, we are having no respite with wave after wave of flood that has wreaked havoc inside the Kaziranga national park and tiger reserve,” said park director P Sivakumar.
Earlier this week nine rhinos had died, but Mr Sivakumar said an animal that drowned in a swollen river near the park on Saturday took the death toll up to 10.
The International Federation of Red Cross and Red Crescent Societies (IFRC) said nearly one-third of Bangladesh had been flooded, with more heavy rain expected in the coming weeks.
In India, at least 6.8 million people have been affected by the flooding, mainly in Assam and other northern states, the IFRC said.
The Bihar government has requested help from India’s air force to airdrop food parcels, authorities said.
Officials have opened relief centres in affected districts, but people have instead chosen to shelter in tarpaulin tents.
In Assam, 96 people have been killed in floods and another 26 have been killed in mudslides.
The Kaziranga park and tiger reserve is home to the world’s largest population of the one-horned rhinos, which faced extinction just two decades ago and are still classed as vulnerable.
Some 2,500 of the world’s total population of 3,000 one-horned rhinos live there.
The floodwaters are making protecting wildlife within the park more difficult, too.
“More than 100 of the 223 security camps inside the sprawling park are still submerged, making day-to-day work of our 1,600 guards really challenging,” Mr Sivakumar said.
The Duke and Duchess of Cambridge wrote to park chiefs: “The deaths of so many animals, including one-horned rhino, are deeply upsetting.”
Last week a rhino that was thought to have been trying to get away from floodwaters stopped traffic on a major road when it laid down and rested its head on the tarmac. It was saved but later died, taking the rhino death tally to 10.
Additional reporting by agencies
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