"Dearly loved and cherished husband of Mary for 57 years,'' the notice read.
"Loving father...and adored 'Granddad Ted' of all his grandchildren and his great-grandchildren.''
A requiem mass will be held on Wednesday.
The All Blacks are due to take on Ireland in a quarter-final match, at the Rugby World Cup in Japan, on Saturday.
The family has deep roots in the Taranaki and New Plymouth areas, where they have a family farm and which the famous All Blacks trio grew up on.
In 2017, locals told sports writer Phil Gifford everyone in the Naki loved the Barretts.
"I've known the grandfather, Ted, for years,'' one local said to him.
"He's a great bugger and the whole family is the same. You won't hear a bad word about them round here.''
In an interview with the Irish Times, in 2017, the brothers' father, Kevin Barrett, revealed that his own father played rugby as a schoolboy, before concentrating on cricket and boxing.
"My dad's parents died when he was 15 and there was only him and his two brothers,'' Kevin Barrett told the newspaper.
He also revealed that Ted Barrett's parents were of Irish descent.
The funeral notice also asks that in lieu of flowers, anyone wishing to donate to the family instead make donations to the Upside Down Education Trust, which helps people with Down Syndrome.
Upside Down is a cause brothers Beauden, Jordie and Scott are all involved with because their younger sister Zara has Down Syndrome.
