The FIA announced the change to its International Sporting Code (ISC) in a statement after a meeting of its World Motor Sport Council in Geneva.
"The ISC had previously determined that the maximum fine amount that the stewards can impose is 250,000 euros," it said.
"This amount has not been reviewed nor amended for at least the last 12 years and does not reflect the current needs of motorsport."
The maximum fine in all other FIA world championships was set at 750,000 euros (£655,000).
"It's a huge amount of money," Ferrari's Charles Leclerc told reporters at the US Grand Prix.
"I have no idea what deserves a one million dollar penalty. I mean, some drivers are making less than that."
Haas driver Kevin Magnussen, whose team have one of the smallest budgets, also struggled to imagine what kind of offence would have to be committed.
"That sounds ridiculous," said the Dane. "Charles can give his watch but I would disappear, never to be found again."
Leclerc had an exclusive Richard Mille watch, which reports valued at more than two million dollars, stolen off his wrist last year.
Live track
Mercedes' seven-times world champion Lewis Hamilton, who was fined 50,000 dollars (£41,300) in Qatar two weekends ago for crossing a live track in an incident that the FIA is reviewing, said it was the first he had heard of it.
"If they are going to be fining a million, let's make sure that 100 per cent of that goes to a cause," added the Briton, whose latest contract will pay him a reported £50 million a year.
"There's a lot of money in this whole industry and there's a lot more we need to do in terms of creating better accessibility, better diversity, more opportunities for people who wouldn't normally have a chance to get into a sport like this.
"So many causes around the world. So, yeah. That's the only way they'll get that million from me."
Now-triple world champion Max Verstappen was fined 50,000 euros (£43,600) in 2021 for touching the rear wing of Hamilton's car after qualifying for the Brazilian Grand Prix.
"If touching a rear wing is 50k then I would like to know what one mill is," said the Red Bull driver.
Formula 1 has seen some of the biggest fines in any sport, with McLaren famously fined 100 million dollars (£82.6 million) and stripped of constructors' points in a 2007 spying controversy involving Ferrari information.
The British team ultimately paid half that amount after the fine was reduced by the loss of revenue resulting from being stripped of their points.
Red Bull were fined seven million dollars (£5.8 million) last year for breaching the sport's cost cap in 2021.
"We just want transparency and understanding. I think already the fines are getting out of control," said Russell.
"It feels like these numbers are being plucked out the air."
In other measures approved on Thursday, the FIA prohibited the unauthorised possession and use of pyrotechnics at FIA competitions.
Dutch fans, in particular, have thrown smoking orange flares at Verstappen's home race.