
It also leaves Britain's Jenson Button without an immediate drive for 2009, although some teams have yet to confirm their lineups.
Brazilian Bruno Senna, the 25-year-old nephew of the late triple world champion Ayrton, had also been tipped to take the place of compatriot Rubens Barrichello at Honda next season.
Honda's exit will leave the multi-billion sport, dominated by carmakers, facing a depleted grid of just 18 cars if no buyer can be found in the extremely tight time-frame available.
It will also prompt fears that other major manufacturers, with their factory production suspended and thousands of staff laid off, could follow Honda's example.
Honda and Toyota Motor Corp <7203.T> have been the big spenders in Formula One in recent years.
Ross Brawn, the former Ferrari technical director who won multiple championships with Michael Schumacher, was hired to run the Honda team at the end of last year.
Despite its huge resources, Honda had a dismal 2008 season and was pinning its hopes on next year's new rules levelling the playing field.
Button, a winner for Honda in Hungary in 2006, scored just three points while Barrichello took 11. The team finished ninth overall.
The last team to leave Formula One was Honda-backed Super Aguri, the tail-enders who folded for financial reasons in April.