Glasgow City Council has endorsed plans to shut most of its museums on Mondays to save at least £100,000 a year.
The Burrell Collection could be one of the museums affected
Eleven museums, including the world-famous Burrell Collection, the People's Palace and Scotland Street School are affected by the decision.
Glasgow is under pressure to make budgets cuts and to fund the £40m cost of an equal pay deal for women.
The Kelvingrove Museum and Art Gallery, which is due to reopen this summer after a revamp, will escape the cuts.
The Gallery of Modern Art will not be affected by the move and the city's newest museum, the Riverside Museum, due to open in 2009, will also be exempt.
However, the McLellan Galleries and St Mungo Museum of Religious Life and Art are among those covered by the cuts.
The council has pointed to the example of many European cities where museums are traditionally closed on a Monday.
But critics fear the decision could have a damaging effect on tourism in a city which was recently named in the world's top 10 destinations.
Glasgow is the first council in Scotland to meet the equal pay demands.
Scotland's councils initially agreed to tackle the issue of equal pay for women six years ago by introducing new pay and conditions structures.
It has been up to councils to implement the national framework in agreement with unions.
Glasgow runs 13 museums and admission to all are free, except for some temporary exhibitions. Last year, they were visited by 1.8 million people.