Paintings and Victorian marble statues held at Carbisdale Castle, a former youth hostel near Ardgay, have been valued at a total of ??500,000.
The art is to be sold at an auction in London next month.
Organisers of the petition on the website change.org want the works should remain in the local community.
They said because the castle and its contents were gifted to SYHA, the association should not be selling off the art to make a profit.
More than 700 people have signed the petition so far.
SYHA shut Carbisdale Castle in Sutherland four years ago because of rising repair costs.
A former stately home, it was known as Castle of Spite because of the part it played in a family feud. The property is also said to be haunted by a ghost called Betty.
SYHA said it would invest money raised from the sale of the castle's artworks in its network of youth hostels.
The 17 sculptures and 36 Italian and Scottish 19th Century paintings will be offered for sale at an auction in London on 20 May.
Auctioneers Sotheby's have put a combined value of ??500,000 on the art.
White marble sculptures from the 1800s to be sold include Andromeda by Florentine sculptor Pasquale Romanelli and Nymph at the Stream by Scottish artist David Watson Stevenson.
It will be the first time in more than a century that the Victorian sculptures have been put on the market.
A petition has been started opposing the sale of artworks by the Scottish Youth Hostel Association (SYHA).