The board resigned under pressure from angry fans on Monday after club president Dobrivoje Tanasijevic quit last week when the 1991 European Cup winners revealed they owed around 23 million euros ($30 million) to creditors.
Many players have not been paid for months, while the club also had its water supply and telephone lines cut for several days in March due to unpaid bills.
"The entire executive board has stepped down and a three-man interim committee will be in charge until June 8, when a new president will be elected," the board said.
"This group worked in extremely difficult circumstances and we now appeal on the players to focus on winning their remaining games this season.
"Red Star owes money to its players, it has owed money before but it has never failed to settle any of its debts, meaning that this squad will also be paid in full in the foreseeable future."
"Red Star owes me a pile of money, I haven't been paid in a long while," he told daily Press and added: "I am not going to sue the club because there is no point."
