Derby's Pickford House Museum is to close to the general public.
The city council has decided to restrict visitors to the house - known as the Museum of Georgian Life and Costume - to advance bookings.
Derby's main museum and art gallery and the Silk Museum, which is the city's industrial museum, will be closed on Sundays and Bank holidays from April.
Councillors have said the closure and reduction in opening hours is a necessary cost-saving measure.
Councillor Hardyal Dhindsa said: "They (the public) are least interested in accessing them on Sundays and Bank Holidays.
"Pickford's House is not going to close - it is an important cultural heritage destination but we need to co-ordinate and target our resources to make sure that most people get the exposure to it and they get a good experience when they get there."
The museum features a Georgian bedroom and dressing room, a servant's bedroom complete with straw mattress, a cellar, pantry and housekeeper's cupboard.
One of the cellars is equipped as an air-raid shelter of the 1940s.
The upper floors feature displays of toys and toy theatres, and a collection of historic costumes and textiles.