"You can imagine how reluctant we are to put it up for sale, but it's a case of doing that or not surviving at all."
The club lost about $34,000 after it mistakenly believed it had booked 2008 British X Factor winner Alexandra Burke as the headline act at its annual summer concert.
It paid for large quantities of food and drink, a top-level stage and lighting system, and what it thought was a $9500 deposit for Ms Burke's performance.
But two weeks before the concert, Paul Johnson, the man who said he had booked the reality TV star, admitted she would not be playing.
Ms Burke's management said they never received a booking request for the event.
Tycroes Rugby Club was founded in 1911 and members hope the jersey's sale will avoid the club's demise.
However, giving up the irreplaceable jersey has divided members, with some vehemently opposed to the sale.
"There's been a lot of debate about it," said financial secretary Ian Thomas.
"Some of the committee were really against it, so in the end it had to go to a vote."
The 1905 All Blacks tour was the first to the British Isles, and the team became known as The Originals. They also toured France and the United States.
The squad journeyed to Britain on board the Rimutaka, stopping at ports Montevideo and Tenerife before arriving at Plymouth, England.
They defeated Devon in their opening game 55-4, a result so unexpected that some British newspapers printed that Devon had scored 55 points.
The team went on to win 34 matches, including tests against Scotland, Ireland and England, only losing to Wales 3-0 in front of 47,000 spectators at Cardiff Arms Park.
The defeat was highly controversial after the referee denied a try to All Blacks winger Bob Deans.
In all the Originals scored 976 points and conceded just 59.
They were the first team to use the All Blacks name and announced New Zealand as a major force in rugby.
