The Briton, who triumphed at the French enduro in 2021, broke his ribs and collarbone in an incident on Thursday and will be unable to take up his place in the #7 Toyota GR010 HYBRID Le Mans Hybrid.
Conway, 40, will be replaced in the line-up for Le Mans on 15/16 June alongside Kamui Kobayashi and Nyck de Vries by Jose Maria Lopez.
Lopez returns to the line-up in the #7 car after being dropped at the end of last season in favour of de Vries.
The Argentinian partnered Conway and Kobayashi to Le Mans victory in ’21, as well as the WEC drivers’ title in 2019-20 and ’22.
Toyota Gazoo Racing has turned to the experienced Lopez rather than Ritomo Miyata, who is the team’s official test and reserve driver for the WEC.
The announcement from the Toyota Gazoo Racing squad on Friday afternoon contained no other details of Conway’s injuries, how they occurred or the likely recuperation time before he can return to the cockpit.
It came little more than a day before the 62-car Le Mans field is due on track for the official Test Day on Sunday, which leads into race week.
Lopez, 41, remains under contract to Toyota and was due to race at Le Mans with sister brand Lexus.
He is driving one of its LMGT3 class RC F GT3s entered by the Auto Sport Promotion team together with Esteban Masson and Takeshi Kimura in the full WEC this year.
Lopez spent six years as part of the TGR prototype squad in the WEC, first in the LMP1 class and then in Hypercar.
His stay with the team had been due to come to an end at the end of 2022: de Vries was scheduled to move up from the role of test and reserve driver last year to join Conway and Kobayashi until he landed what turned out to be a short-lived opportunity in Formula 1 with AlphaTauri.
Miyata is racing for the Cool Racing LMP2 squad at Le Mans as part of a programme encompassing the European Le Mans Series.