Cyclone Amphan has killed at least 22 people in Bangladesh and left many displaced in the country's coastal areas.
The refugees, including 15 women and six children, landed on Bhasan Char island on Saturday and are believed to be from one of several boats stuck at sea.
Health and police personnel would visit them to check their health status, police sources said, adding that no positive case has been reported with regard to Rohingyas under the Rachakonda police.
The money would go to respond to the needs of approximately 855,000 Rohingya refugees from Myanmar and over 444,000 vulnerable Bangladeshis, UN said.
Bangladesh is home to nearly a million Rohingya including 740,000 who fled a military crackdown in Rakhine state in August 2017 that the UN has called ethnic cleansing.
Tensions are rising in south-east Bangladesh two and a half years after hundreds of thousands of Rohingya refugees fled a military offensive in Myanmar.
With the monsoon over and seas relatively calm, increasing numbers of Rohingya Muslims are once again risking their lives attempting to reach Malaysia or Indonesia.
Rohingyas will be barred, says Amit Shah; Citizenship (Amendment) Bill drives past Lok Sabha comfortably
Shah referred to the decline of minority population in Pakistan and Bangladesh, and stressed that in Pakistan in 1947, the minority population was 23 per cent which came down to 3.7 per cent in 2011.
Nearly a million Rohingya, including some 740,000 who fled a 2017 military crackdown in Myanmar's Rakhine state, are now living in squalid camps.
More than 1.1 million Rohingya are currently residing in Bangladesh with 700,000 of them coming following the crackdown by the Myanmar Army in August 2017.
It accuses Myanmar of breaching the UN Genocide Convention through a bloody military campaign which has driven hundreds of thousands of people from the Rohingya minority into neighbouring Bangladesh.
More than 600,000 minority Rohingya Muslims have fled to Bangladesh to escape violence in Myanmar's Rakhine State since August 25 last year.
Some 700,000 members of the Muslim minority have fled Myanmar since August to escape a bloody military crackdown.
Bangladesh will begin relocating around 100,000 Rohingya refugees to a desolate island off its southern coast despite warnings the site is prone to violent weather.
Canada announced targeted sanctions in February against a Myanmar general who led the army crackdown.