"We need to contain these cases, while there are still only a few of them," said Indonesian health minister Budi Gunadi Sadikin, after the first two cases of the variant reported in the southeast Asian nation on Monday.
Neighbouring Malaysia said on Sunday it had detected its first case of the Indian variant, days after imposing a ban on flights from the country.
On Monday, Taiwan said that except for its citizens, all those who had been in India in the 14 days prior would be barred from entering its territory, while returning Taiwanese face 14 days in centralised quarantine facilities.
The move comes after Australia took a more drastic measure last week, banning the entry of residents and citizens who have been in India in the previous two weeks, threatening fines and jail for any who disobey.
It was the first time Australia has branded citizens' return home a criminal offence.
Australia defended the ban, which took effect on Monday, saying it had a "strong, clear and absolute" belief that the move was legal.
"It's a high-risk situation in India," Health Minister Greg Hunt told a televised news briefing.
"The strong, clear view is that there has been no doubt in any of the Commonwealth advice about this."
Philippine officials warned that they could not rule out the possibility of an India-like Covid-19 crisis, saying last week's decision to ban entry of arrivals from India aimed to keep it from becoming a reality.
"It is possible for it to happen here if we don’t intensify responses," Health Undersecretary Rosario Vergeire said.
"When we look at what is happening in India, it is happening across the globe... What’s different is the intensity of it."
The World Health Organisation designates the variant as being "of interest", suggesting it may have mutations that would make the virus more transmissible, cause more severe disease or evade vaccine immunity.
Other strains with known risks, such as those first detected in the Brazil, Britain and South Africa, have been categorised as "variants of concern," a higher threat level.