Lady Hillary was the patron of the New Zealand Nepal Society and served as the Honorary Consul-General of Nepal to New Zealand for many years.
Her death comes just days after the 71st anniversary of Sir Edmund's summit of Mount Everest with Sherpa Tenzing Norgay. Sir Edmund was the first person to reach the top of the world's highest peak.
In a social media post, Dinesh Khadka, the Honorary Consul of Nepal for Auckland, said he extended his "deepest condolences" to Lady Hillary's family.
"Lady June Hillary was an exceptional individual whose contributions to Nepal and the Nepalese community in New Zealand were immeasurable," he wrote.
"Her dedication ensured that Nepal's rich heritage and traditions were celebrated and appreciated in New Zealand."
Khadka said Lady Hillary advocated "passionately" for the Nepalese community.
"Her unwavering commitment to the welfare of the Nepalese people has left a lasting impact on our community.
"Lady June's compassion, dedication, and service legacy will continue to inspire us all."
Lady Hillary married Sir Edmund in 1989 following the death of his first wife, Louise, and daughter Belinda in a plane crash. She was earlier married to Peter Mulgrew, who was a close friend of Sir Edmund.
Three years later, Lady Hillary stepped down from the Himalayan Trust - a non-profit established by her late husband in the 1960s - following clashes with his surviving children, Sarah and Peter.
The trust said it was with "great sadness" that it farewelled Lady Hillary.
"June was involved in the Himalayan Trust since its beginnings through her friendship [with] Ed and Louise," it wrote in a social media post.
"She had a deep fondness for the Himalayas and the people of Nepal."
Lady Hillary was "key" in supporting Sir Edmund's work with the trust in the later years of his life, the trust said.
"June was wonderfully funny, caring and had a tremendous sense of style.
"Arohanui June. You will be missed."
The Nepal New Zealand Friendship Society of Canterbury expressed its "deepest sorrow" at the loss of Lady Hillary.
She was her late husband's "steadfast support system", it said.
"May her soul find eternal peace, and may her memory continue to inspire and unite people."