The box has been passed down through many generations of the same family, but was being put up for auction with several other antique items because the owner had recently moved into a retirement home and had nowhere to put it.
Auctioneer Barry Forno said it was one of those "wonderful and special" items, rarely seen in auctions.
"It's a significant piece of Otago history. Items like this are extremely rare. We've never had anything of this significance in my 36-year career."
The box contains a worn inscription which is mostly indecipherable. But the words "Robt Burns, May 8th 1786" and "Auld lang syne" are clear.
Former Otago Settlers Museum curator Michael Findlay believed the box may have been given to Burns by William Tytler, who assisted Burns in collecting verses for volumes of his Scots Musical Museum.
Mr Forno said the box would attract bids from all over the world, but no-one really knew what price it would fetch in the auction. The highest bid would be referred to the vendor and he would have the final decision about whether he would "let it go or keep it".
What is snuff?
• Snuff is any powder prepared for sniffing - usually powdered tobacco.
• Tobacco snuff is made from the leaves, and sometimes the stalks, of tobacco plants which are disintegrated into a coarse powder. It is then ground in a mill and sieved.
• Various essential oils are added for flavouring, and it is stored in airtight containers to allow the flavour to permeate.
