Jean Todt is worried that the upper tiers of motor racing could lose the support of car manufacturers amid the corona crisis.
With countries locked down, racing series halted and an economic recession looming, the FIA president admitted the manufacturers may need to rethink their commitments.
"I don't think that the priority now for a manufacturer is to secure continuity in motor racing," he told Auto magazine.
"I'm sure some teams, suppliers and manufacturers may have to review their programs. They might be constrained to stop.
"I hope team owners and sponsors will keep the motivation. We must encourage them to feel they still like it and need it. On that, we have a responsibility. That's why we should listen to everybody.
"We must be humble. Even if we love motorsport, it is not essential for society. So we have to ensure that we make proper choices and wise decisions. In fact, what's needed is a complete rethink of how we go motor racing.
"We could talk of a 'New Deal' approach, like America had after the Great Depression," Todt said, referring to the government programs instigated by Franklin D. Roosevelt.
A big complication for F1 in particular is that many car manufacturers involved in motor racing are choosing the affordable and 'green' option of Formula E.
"I feel sorry for the guys running F1 now, as they have to consider the impact of Formula E," former F1 supremo Bernie Ecclestone told Autocar.
"I would have buried it. It would have saved all the arguments. It wouldn't have happened if I had been there.
"But now everyone is only talking about electric cars, so it would be a bit of a courageous thing now to go against it."