A tourist attraction employing nine people in New Abbey is facing the axe as a result of government budget cuts.
A review of the future of The National Museum of Costume is underway with a final decision due next month.
The Shambellie House attraction is part of National Museums Scotland, which is funded by the Scottish Government.
A spokesperson for NMS said: We are currently conducting an internal consultation. The museum has a very large operational spend per visitor and low visitation.
It attracts 0.6 per cent of the total visits to our group of museums and the board of trustees has concluded that it can no longer continue to operate the site at this level.
We will discuss the way forward with staff and trade unions, and until those discussions are complete we are not in a position to make a public statement.
Dumfries and Galloway MP Russell Brown has written to Fiona Hyslop, the cabinet secretary for culture and external affairs, calling on her to step in and protect the museum.
He said: I was very concerned to hear the National Museum of Costume at Shambellie House is under threat because of SNP budget cuts.
It is an important asset to Dumfries and Galloway and its possible closure will come as a big blow to staff, as well as local people and visitors.
The museum may be small compared to others in the country, but it is significant for our region.
If National Museums Scotland is to be a truly national organisation then it needs to represent the whole of Scotland.
He added: The closure of the National Museum of Costume would send a terrible signal about how our region is viewed.
Yet again, the SNP seem too ready to forget about Dumfries and Galloway.
We must fight to protect what we have in our region and I wont stand back and watch as we lose services.
The museum opens daily from April to October and provides visitors with an opportunity to view collections of Scottish style throughout the ages from the Victorian era to the 20th century.
Abbey ward councillor Tom McAughtrie added: Jobs are jobs, even if they are seasonal.
This is a big employer in New Abbey and I hope they consult with local people.
I hope the council will get involved.