The French race, usually held in June at the Sarthe circuit and now in its 88th edition, was attended by 250,000 people in 2019, with a large number coming from Britain.
"Sadly, the world’s greatest endurance race will be run this year with no spectators trackside," Pierre Fillon, president of the Automobile Club de l'Ouest (ACO), said in a statement.
"Given the constraints involved in organising a festival-scale event over several days in the current situation, we have opted with the local government authorities to hold the race behind closed doors.
"We know that our fans will be as disappointed as we are by this decision but, with public health in the balance, it really wasn’t a difficult call to make."
Toyota are the defending champions.