Withdrawal from the race means the team defaults on the terms of the Concorde agreement, which ensures competing teams a slice of TV revenues and other financial benefits.
Said a statement from the team, led by Tom Walkinshaw: "The team remains in detailed discussions with potential investors.
"In the light of this, Arrows has been advised to do nothing that could interfere with these discussions and that the Orange Arrows team should not compete in the Hungarian Grand Prix this weekend.
"Arrows hopes to be in a position to make a further statement in the near future."
Former British American Racing team boss Craig Pollock has gone on record as having put in a bid for the team, and the firm behind the Red Bull drink - a sponsor of the team - is also believed to be interested.
However, according to a report in today's Financial Times, even a successful takeover may not be the end of Arrows' troubles, with rival team owners likely to appeal against any new set-up, disputing its claims for a cut of Concorde revenues.
It is believed staff at the team's Oxfordshire, England, base have been told they will not be paid for July, while its engine-supplier Cosworth Racing had demanded $1.6m by noon GMT today to release engines for the team's cars.
