Sanchez, who has effectively been in charge of the design and development of Ferrari's F1 cars for the past two seasons, has been at Maranello for more than 10 years.
He originally joined the squad from McLaren in October 2012 as principal aerodynamicist, before replacing Dirk de Beer as chief aerodynamicist in 2016.
The Frenchman was then promoted to lead the entire aerodynamics department in 2019, before his promotion to chief engineer, head of vehicle concept in 2019.
He, therefore, took charge of work on last year's F1-75 and the current SF-23.
Sanchez was one of the key figures of Ferrari's era under Mattia Binotto and was credited with playing an influential role in the team's return to form in 2017 as he and Simone Resta turned the SF-70H into a race winner.
The timing of Sanchez's departure is far from ideal, with Ferrari already facing a challenge in trying to work out how to close down the gap to Red Bull after the disappointment of the season-opening Bahrain Grand Prix.
With senior figures at other teams all likely to need to see out a lengthy period of gardening leave, Ferrari will almost certainly need to shuffle staff internally to make up for his absence in the short term.
Sanchez himself is also likely to need to take a lengthy period of gardening leave too before being able to work elsewhere, with his next destination not yet confirmed.
The news of Sanchez's departure comes as Ferrari team principal Fred Vasseur has made clear his desire to push every department at Maranello to strive to do better.
Speaking ahead of the start of the season, Vasseur said that nobody would escape his request to lift their game.
"Every single area of every single team has to improve," he said. "This is important. It's the DNA of my business.
"We need to have the approach to try to do a better job tomorrow than today. And it's not just the race engineer or the chief of aero, it has to come from every person of the company including the production.
"If the guy on the production can produce a bit faster, or a bit lighter or a bit cheaper, it will be a support for the development of the car.
"We have to send this kind of mindset to every single team member."
After a difficult Bahrain GP weekend, where Ferrari was outclassed by Red Bull and beaten by Aston Martin, Vasseur promised a deep analysis of where things had gone wrong.
"It's never good to start with a DNF and I would've preferred to finish for sure," he said in the wake of Charles Leclerc's retirement.
"But I want to stay consistent in my position.
"I told the team before the test in Bahrain two weeks ago that the championship won't be over in Bahrain. It doesn't matter the result in any case: and it was true for the winter test, and it's true for [the race] today.
"The most important thing now is to be able to have a clear picture of the situation where we are failing, and to do a proper analysis on this and to conduct a stronger response."
