The 65-year-old singer was presented with a key to the city in 1990, following a performance at the Formula One Grand Prix.
WENN reports that the key and a commemorative plaque have now been posted for sale on eBay, inciting strong words from Adelaide's government officials.
Former mayor of Adelaide Steve Condous, who presented the key to Cher, said: "I think that's pretty poor. I'm disappointed. I would have thought that getting the key to a city like Adelaide would have had some value to her, but obviously it doesn't because she wouldn't have got rid of it... If she didn't want to keep it, she should have returned it back to the city."
Current mayor Stephen Yarwood added: "[I am] exceptionally disappointed… I just think that it is more a reflection on her than the city of Adelaide. It must be very embarrassing for her if she is selling it because she needs the money."
The online auction, which ends on Thursday, currently has reached a bidding price of over $80,000 (£49,600).
Cher, who recently attended the GLAAD Media Awards where son Chaz Bono was honoured, has yet to comment on the auction.
Watch Cher sing 'The Power' live in Australia below: