Nepal, Bangladesh and Pakistan have all experienced recent record death rates due to Covid-19, the IFRC said in a release.
With a population of 30 million, Nepal has 1,600 intensive care beds and fewer than 600 ventilators, and 0.7 doctors per 100,000 people, according to a Reuters report citing ActionAid Nepal.
Bradey is credited as the first woman in the world to climb Mount Everest without supplementary oxygen in 1988.
In her appeal to the Government, Bradey said Nepal and New Zealand have a "long and strong association" especially through Tenzing Norway and Edmund Hilary's first ascent of Mount Everest in 1953.
"New Zealanders regularly trek in Nepal ... and have established many smaller lower profile agencies who look after regions or villages in Nepal suffering from significant hardship," she wrote.
"Nepalis greet New Zealanders with extra warmth borne of this history."
She says she has heard back from the New Zealand ambassador-designate to Nepal, David Pine, who told her they were aware of the unfolding situation in Nepal and looking at options for New Zealand to help.