The 382 survivors on board would be sent to Myanmar, the official said.
Video footage showed a crowd of mostly women and children, some stick-thin and unable to stand, being helped to shore. One emaciated man lay on the sand. A refugee told a reporter they had been turned back from Malaysia three times.
Rohingya are not recognised as citizens of Buddhist-majority Myanmar and complain of persecution. Myanmar denies persecuting Rohingya but says they are not an indigenous ethnic group but immigrated from south Asia.
More than a million live in refugee camps in southern Bangladesh, the majority having been driven from their homes in Myanmar after a 2017 military crackdown that the army said was a response to attacks by Rohingya insurgents.
For years, Rohingya have boarded boats organised by smugglers in the hope of finding refuge in Southeast Asia. The voyages usually take place in the dry season, between November and March, when the sea is calm.
Rights groups fear restrictions across the region in response to the coronavirus could lead to a repeat of a crisis in 2015, when a crackdown by Thailand meant smugglers abandoned their human cargo at sea on crowed, rickety boats.
Chris Lewa, director of the Arakan Project, said she believed several more boats were stranded.
“Rohingya may encounter closed borders supported by a xenophobic public narrative,” she said in a message.
“COVID-19 cannot be used to deny access to territory to desperate refugees in distress. Another maritime crisis in the Andaman Sea as in 2015 is unacceptable.”
A police official in Malaysia’s Kedah state told Reuters several boats were trying to reach its shores and monitoring had been stepped up.
A police official in southern Thailand said five boats carrying Rohingya had been spotted off the coast of Satun province late on Monday. It was not possible to independently confirm this.