Indigenous people displaced across the border in neighbouring Brazil and Colombia are "at risk" as the novel coronavirus sweeps through South America, said the UN refugee agency.
The UNHCR said the number of suspected and confirmed COVID-19 cases was increasing, while the first deaths had been reported among indigenous communities.
The agency said there were almost 5,000 indigenous Venezuelans displaced in Brazil, mainly from the Warao ethnic group, but also from the Enapa, Karina, Pemon and Ye'kwana communities.
"With COVID-19 hitting this Amazon region hard and Brazil emerging as an epicentre of the pandemic, UNHCR is worried that many may struggle without adequate health and sanitation conditions," said spokeswoman Shabia Mantoo.
Meanwhile, a number of indigenous groups live around the Venezuelan border with Colombia.
"While their ancestral homes straddle both countries, many have not been able to regularise their stay in Colombia and are undocumented. Some now also face threats from irregular armed groups who control the areas where they live," said Mantoo.
She said many were in isolated areas, lacking access to health services and clean water, while others were in cramped dwellings.
"Most of the border indigenous groups are threatened by physical and cultural extinction because of insufficient food and severe malnutrition that can increase the risk of contagion," said Mantoo.
Meanwhile, national lockdowns have stopped many of their livelihood activities, and faced with increasing poverty, some were having to peddle goods on the streets.
"Not only does that expose them to the risk of infection but also stigmatisation and discrimination for perceived inability to comply with lockdown and physical distancing measures," Mantoo said.
The UNHCR said increased resources were urgently required to continue the "life-saving" work being done by host countries and humanitarian organisations and urged countries attending an upcoming donor conference to pledge their financial support.
"Alarmingly, the regional response plan for refugees and migrants from Venezuela is currently just four-percent funded," said Mantoo.
The European Union and Spain are to host the online donor conference on May 26 to support millions of migrants fleeing Venezuela.
The event aims to mobilise funds and raise awareness of the plight of more than five million people who have escaped the political and economic chaos engulfing Venezuela under President Nicolas Maduro.