Waddesdon Manor’s plant centre is to close at the end of February.
There are between 10 and 14 staff employed at the centre, which includes the Glasshouse Café.
A centre representative said: "There's lots of reasons why we're closing but the main one is we've been making a loss every year."
The National Trust created the plant centre on the site of the Victorian kitchen gardens. A sale begins on 17 January.
The Rothschild family bequeathed the house and grounds to the National Trust in 1957.
Waddesdon Manor received 317,000 visitors in 2012, according to latest figures from the Association of Leading Visitor Attractions.