The museum, based at Shambellie House, near New Abbey, Dumfries, is now closed for the winter and will not reopen for the spring season.
Bruce Minto, chairman of the Trustees of National Museums Scotland, said: "It is with great regret that we have taken the decision to close the National Museum of Costume. While this has been an extremely difficult decision for the Board of Trustees, we are clear that in the current challenging financial climate it is a necessary part of a range of cost savings which ensures the long-term future of our national collections."
Dr Gordon Rintoul, director of National Museums Scotland (NMS), added: "The low number of visitors to the site, along with the high operational costs, is simply not sustainable. In addition, the domestic layout of Shambellie House places limitations on it being used effectively as a national museum."
The NMS said the costs of the museum, which opened in 1982, are £220,000 a year, but it attracts only 15,000 visitors a year, 5000 of those to the cafe and shop.
There are four permanent staff members.
The costumes at the museum will be stored at the National Museums Collection Centre in Edinburgh.
A display of some of the costumes is planned for the new Art and Design galleries which are to open in 2016 at the National Museum in Edinburgh.
The Scottish Government will now spend £20,000 trying to finding a new use for Shambellie House.
Fiona Hyslop, the Culture Secretary, said: "I am keen that NMS helps to find a solution for the future of the site, working in conjunction with Dumfries and Galloway Council."