Jill Guy, who owns and operates the cafe at the Otago Museum, is not optimistic her lease will be extended, despite about 2000 people having signed a petition to support its continuation.
Museum authorities say Ms Guy had initially operated on a six-year lease, which was extended by a further three years in 2006, and that the museum will run its own cafe when the lease expires at the end of this month.
Ms Guy said that when she had been away on a recent trip to Canada, cafe staff members had started a public petition calling for her business to be saved through an extension of the lease.
The response had been "absolutely wonderful" and "hugely successful", and she understood about 2000 people had signed.
She had built up a "huge business", had paid the museum $80,000 in rent last year, and the public believed it was "ridiculous" for the museum to start running its own cafe, she said.
Museum authorities recently put up posters in the downstairs foyer, near the cafe, pointing out that the museum would continue to operate a cafe after the lease expired.
An information sheet, provided from the nearby main counter, states that the cafe tenant had been advised in writing when the lease had been renewed for three years in 2006 that no further rights of renewal would be granted and the lease would end on November 30.
In the poster, museum chief executive Shimrath Paul invites museum visitors to fill out a "tell us what you think" form about ideas for the new cafe.
Ms Guy said many cafe users had already made their views clear that they wanted the existing cafe to continue.
Museum director, exhibitions, development and planning, Clare Wilson said several New Zealand museums, including Te Papa, ran their own cafes.
More than half the money required to pay for the Otago Museum's operating spending had to come from earned income in order to minimise the burden on ratepayers.
Enabling the museum to gain further income through running a cafe would clearly benefit museum visitors, she said.
In 2000, the museum had funded the relocation, creation and fit-out of new cafe premises as part of a major museum redevelopment.
The lease of the cafe was a commercial arrangement, not a right or a gift, and the tenant could establish a business elsewhere, she said.