Williams are bottom of the 2022 constructors' championship
The team missed the 31 March 2022 deadline to submit its 2021 accounts and are the first to be punished under the cap since its introduction last year.
Williams had informed rule makers of the problem ahead of time, the FIA said.
The cap has been reduced to $140m this year from $145m (£114m) in 2021.
The cost cap was created to limit how much an F1 team can spend during a calendar year in order to compete.
Williams were found to have committed a "procedural breach" of the rules and had to bear the costs incurred by the cost cap administrators as well as the fine.
The development comes as teams fight for an increase in the cost cap this season, which will go down again to $135m in 2023.
But a number of leading teams have argued that global inflationary pressures mean they should be given a representative increase.
Red Bull team principal Christian Horner has said some teams might have to miss a number of races later in the season if governing body the FIA does not grant the concession.
However, other teams have rejected the idea, with Alpine arguing that those struggling to meet the cap should simply spend less money on development.
Ferrari team boss Mattia Binotto said at last month's Monaco Grand Prix: "I'm pretty sure that at some stage we will go over.
"In the regulations, there is a threshold, which is at 5%. If you do not exceed the 5%, on the top of what's the budget cap threshold, it will be considered a minor breach.
"And what's a minor breach in case of force majeure? What will the stewards and the FIA decide on that, in terms of penalties?
"No idea - but I don't think there is any way for us - and for many teams - simply to stay within, and even laying-off people, I don't think that's a good and right choice."
Mercedes F1 boss Toto Wolff said: "Having a raging war in the Ukraine and the consequences it had on energy prices is not something that could be foreseen and there needs to be some kind compromise between the teams who are against an inflationary adjustment and those who are for it."
Alpine team principal Otmar Szafnauer said: "Most teams do their budgets in November, December timeframe, for the following year and we are no different. And at that time, inflation was already at 7+%. RPI in England was 7.1, 7.2%.
"We took that into consideration when we did our budgets and laid out all the development work that we were going to do. And we're still within it, even though freight was a little bit more expensive than we thought. And we plan to be there at the end of the year. And we'll adjust the development accordingly."
Alfa Romeo's Frederic Vasseur added: "If we have some increase on energy or freight, the best solution is to switch off the wind tunnel to stop bringing updates every single weekend."
-- Courtesy of BBC Sport