Steve Hood is understood to have left the company after his role as head of marketing was axed.
Andy King, the team's head of acquisition and strategic development has assumed his responsibilities. These included overseeing relationships with sponsors, such as title backer Orange.
Arrows faces an uncertain future after it failed to compete in the past two Grand Prix competitions.
There was speculation last week that US businessman Carl Smith was interested in bidding for the team, while motor-racing entrepreneur Craig Pollock has also been linked with a bid.
As well as Orange, Arrows' sponsors include Red Bull, which is keen to launch an all-US F1 team (Marketing, June 27). The future of Orange's sponsorship has also been the subject of speculation.
Arrows' misfortunes come at a time of uncertainty for the sport. Concerns have mounted about the sport's appeal to audiences bored by Michael Schumacher's and Ferrari's dominance of F1. It also has to face up to the consequences of the abolition of tobacco sponsorship.
Reports last weekend suggested Ford is to withdraw from F1 because of Jaguar's lack of success, although the US car giant has denied the team is up for sale.