The New Zealand Herald understands he has had a mild stroke.
Mr Moore has had other health problems and had a heart valve operation a year ago.
He has been in the diplomatic post in the US capital city since 2010 and even without ill-health, he and his wife, Yvonne, had been widely expected to return home this year.
Foreign Minister Murray McCully would not confirm whether he had suffered a stroke but a spokesman said: "I am aware that Ambassador Moore is unwell. Out of respect for his privacy, I won't be providing further comment at this time."
Trade Negotiations Minister Tim Groser is expected to become ambassador to Washington later in the year, after the Trans Pacific Partnership trade talks have run their course.
Mr Moore is a former Director-General of the World Trade Organisation. He entered Parliament in 1972 when he was elected to represent the Auckland suburb of Mt Eden and later represented seats in Christchurch.
He became leader of the Labour Party in 1990 and was Prime Minister for a few months before National and Jim Bolger won the election that year. Mr Moore remained Opposition leader for three years.
During his time in Parliament he also held the positions of Foreign Minister, Trade Minister and Deputy Finance Minister.
