Sri Lanka on Thursday became the latest of India's neighbours to seal its borders with the South Asian giant as it battles a record coronavirus surge.
Bangladesh and Nepal have also banned flights and sought to close their borders with India, where a huge rise in numbers in the past three weeks has taken deaths past 230,000 and cases over 21 million.
All three countries are fighting their own pandemic surges, which Red Cross leaders have described as a "human catastrophe".
The Sri Lankan government banned flight passengers from India entering, as the country reported its highest daily toll of 14 deaths and 1,939 infections in 24 hours.
Sri Lanka's navy said it had stepped up patrols to keep away Indian trawlers, adding that on Tuesday it stopped 11 such vessels which had crossed the narrow strip of sea dividing the two neighbours.
Bangladesh halted all international flights on April 14 because of its own surge and shut its border with India on April 26.
It has reported 11,755 Covid-19 deaths and 767,338 cases, but experts say the real figures are higher in all South Asian countries.
Bangladesh has had 10 million vaccine doses from India, but the supply has been halted and the government is now negotiating to get Chinese jabs.
Nepal suspended international flights a week ago, until May 14.
Just two return flights a week are allowed to India, to bring back stranded nationals. Most border crossings are also closed and only returning Nepalis can use those still open.
Many hospitals in Nepal are overflowing with Covid-19 patients, according to the International Federation of Red Cross and Red Crescent Societies (IFRC).
"Southern towns near the Indian border are unable to cope with the growing number of people needing medical treatment," it said. "Nepal is recording 57 times more cases than this time last month."
Nepal, Bangladesh and Pakistan are all experiencing record Covid-19 death rates, it added.
"We need to act now and we need to act fast to have any hope of containing this human catastrophe," said IFRC Asia-Pacific director Alexander Matheou.
"This virus has no respect for borders and these variants are running rampant across Asia."
Even the luxury tourist destination of the Maldives has tightened restrictions for Indian visitors, insisting on negative test results on entry.
India is the largest tourist market for Sri Lanka and the Maldives, both of which now face huge losses from the fast-spreading Covid-19 new wave.
Sri Lanka has reported 117,529 infections with 734 deaths since the start of the pandemic. The Maldives has reported 32,665 cases with 74 deaths.