The crisis has caused the start of the season -- initially set to begin in March -- to be delayed, with the Canadian Grand Prix recently becoming the ninth race to be either postponed or canceled.
Speaking to reporters on a video conference call on Wednesday, Seidl said the sport risked losing teams unless changes were made.
"It's not just the fear, I think it's reality," he said, as reported by Reuters. "There's a big risk that we could lose teams through this crisis.
"I think the crisis we are in now is, let's say, the final wake-up call ... the sport which was unhealthy before and not sustainable has now reached a point where we need big changes, drastic changes."
"I don't see any signs that Formula One will not exist in the next year," he added. "The biggest risk that I see is that we will lose teams if we don't take decisive actions now."
Amid much confusion, the season opener in Australia was eventually canceled last month after a member of the McLaren team tested positive for coronavirus.
The Monaco Grand Prix -- the jewel in the crown of the F1 season -- has also been canceled and a further seven races postponed.
Formula One rules stipulate that a minimum of eight races must be held for a season to be classified as a world championship.
With the season on hold, McLaren -- along with four other British-based teams -- has opted to furlough a number of its workforce and use a UK government job scheme that pays employees placed on temporary leave 80% of their wages, to a maximum of £2,500 a month ($3,122).
Formula One has also temporarily furloughed half of its employees, it was announced on April 7, and its directors and executives -- including chief executive Chase Carey -- have taken a voluntary 20% pay cut.
The cancellations and posponements have already hit teams hard, with most of their revenues coming from broadcasting deals, race hosting fees and sponsorship, reports Reuters.
Teams have already agreed to a $150 million budget cap for the 2021 season in an attempt to level the playing field, but Seidl is in favor of a further reduction to $100 million.
"It's important to make now big decisions, to make another big step in terms of the level of the budget cap of the future," said Seidl.
"We think it's absolutely important now with all the financial losses that we will face this year, the magnitude of which is still unknown.
"I think $100 million is a good number to run a Formula One team in the way we want to see Formula One."