Since 2019 the regulations have allocated an extra point provided the driver finishes in the top 10 - a potentially significant consideration in a 24-race season like 2024.
The FIA said ahead of the US Grand Prix in Austin that changes to the 2024 and 2025 sporting and technical regulations were approved by its World Motor Sport Council at a meeting in Paris and by video conference.
As well as removing the point for the fastest lap, the requirement for fielding a young driver during free practice will increase from once per car per season to twice per car per season.
The fastest lap point can be crucial when the championship is on a knife-edge but it has also become a part of strategy, sometimes controversially when used by teams with common ownership.
At last month's Singapore Grand Prix, RB's Australian driver Daniel Ricciardo pitted at the end for fresh tyres to set the fastest lap in what was likely the last race of his F1 career.
The move did not bring him a point, because he was outside the top 10, but benefitted Red Bull's Max Verstappen by taking the point away from McLaren rival Lando Norris, who had previously been fastest.
Norris, 52 points behind Verstappen with six rounds remaining, has taken four points from fastest laps so far this season - including three of the last four - to the triple champion's two.
"I would say probably it's the right thing to get rid of it because it's not really relative to the speed, like who's the fastest out there," said Sauber driver Valtteri Bottas at the Circuit of the Americas.
"It's always depending on strategy, who stops the last basically will get it, so it doesn't tell much. I think even with our car, we could sometimes maybe get it if we stop before the last lap and go all out."
Sauber are the only team yet to score a point this season.