The ACO has decided against running the test day, which normally takes place two weekends before the race, for multiple reasons, according to its president, Pierre Fillon.
He explained that it had been forced "rethink our priorities" as a result of the coronavirus pandemic, which has already resulted in major changes to the world motorsport calendar.
The 24 Hours motorcycle endurance race on the Le Mans Bugatti circuit has been put back from April to September 5-6.
Fillon said that "holding two major events within three weeks of each other is a challenge" and that it was necessary to "sacrifice the test day".
He explained that there was also a desire not to "overtax" competitors in what is likely to be a crowded schedule for the FIA World Endurance Championship and the European Le Mans Series after the resumption of racing.
Fillon pointed out that "the test is not as old as the race and has been skipped on many occasions".
"We've never been faced with a situation like this before," he added. "An unprecedented situation calls for exceptional measures."
A full schedule for Le Mans week is due to be announced at a later date, while the ACO is due reveal whether the postponed Spa round of the 2019/20 WEC will be rescheduled and a revised calendar for the 2020/21 season in early April.
The Le Mans test day was a regular part of the international sportscar schedule in the 1960s and early 1970s. It made a short-lived comeback in the 1980s before returning in 1993, briefly becoming a competitive pre-qualifying event.
The only years since then that it did not take place were in 2009 and '10, when it was cancelled as a result of the economic downturn. It returned in 2011 with a date at the end of April, before moving back to its slot two weeks prior to the race.