The library said closing on Saturdays was "unfortunate but necessary"
The National Library for Wales in Aberystwyth is to close to the public on Saturdays from next April.
The library's board said it had to save £250,000 in the next financial year and blamed a "steady decrease in its budgets over recent years".
Library president Dafydd Wigley said it was "in an impossible situation".
The Welsh Assembly Government said the library had been given an increase in its draft budget and was "disappointed" the library had "chosen this option".
The library said its "unfortunate but necessary decision" was part of a package of measures it had been forced to put together to make the six-figure saving in the coming financial year.
In a statement released after the board's decision on Friday, the library said that as well as losing use of the reading rooms on Saturdays, the public's access to the exhibitions, restaurant and shop would also go.
Andrew Green, librarian of the National Library of Wales, said: "This was a very difficult decision to make, but necessary to maintain the other services the library offers."
Mr Wigley, the former Plaid Cymru leader, said: "The library has been put in an impossible situation and the people of Wales are the ones that are going to suffer, losing the services of one of its most important institutions on the only day of the week on which many can visit."
Aberystwyth mayor Sue Jones-Davies said: "I think it's very sad that this is happening.
"I understand the library might be suffering financial problems, but Saturday is the only time when the average person can visit.
"If we're trying to encourage tourism to the town it's a decision I would not generally welcome."
Historian Dr John Davies, author of A History of Wales and one of the editors of the new Welsh Encyclopaedia, described the national library's decision as "rather sad news".
He said he had visited libraries in America which were open 24 hours a day.
He added: "It's curious we have all-day and all-night shopping, but we don't have something more intellectual to do such as visiting the national library.
"I understand the sort of financial constraints the library is facing and I sympathise with its staff who have to work on Saturdays - you'll never meet a more dedicated body of people."
The National Library of Wales is funded by the Welsh Assembly Government.
A Welsh Assembly Government spokesman said: "The National Library have been given an increase in the draft budget for next year.
"We acknowledge that financially this is a very difficult and challenging time for public bodies.
"However we are disappointed that the library has chosen this option which will particularly impact on its users."