Halberg passed away at the age of 89, the New Zealand Herald has confirmed.
Halberg was best known for winning the 5000m gold medal at the 1960 Olympics in Rome, while he also won gold at the Commonwealth Games in 1958 and 1962 in the three miles race.
He also became the first Kiwi to break the four-minute mile.
After his sporting career, Halberg set up The Halberg Trust, which continues to support children with disabilities in sport under its new name the Halberg Disability Sport Foundation.
The Halberg Awards, New Zealand’s most prestigious sports awards, are named in his honour in recognition for his work in sport and children with disabilities.
He was knighted in 1988 for services to sport and disabled children.