"We opened insolvency proceedings to save the club," Rapid's majority shareholder George Copos told reporters. "We're doing everything in our power to save Rapid."
Three-times Romanian champions Rapid and city rivals Dinamo, who have won the league 18 times, are among nine European clubs facing punishment from UEFA over payment arrears to other teams, their staff or tax authorities.
Rapid, who played in the Romanian Cup final in May, have spent heavily in recent years but their players have not been paid for several months.
"The difference between revenue and expenditure goes to 5 million euros per year," said Rapid president Constantin Zotta. "It's terrible."
The move could mean the end of professional football for Rapid as Romanian regulations do not allow an insolvent club to have a first-division licence.
"If they enter into any form of insolvency, they will not get a licence for next season," said Romanian Football League president Dumitru Dragomir.
On Monday, Dragomir said that seven first division clubs were on the brink of collapse due to spiralling debts.
He accused the government of not supporting the sport. "We are the only country in the world that pays VAT to the players," Dragomir said. "Taxes are paid two or three times."
Dragomir did not name the teams but local media said that Dinamo, Petrolul Ploiesti, Brasov, Universitatea Cluj-Napoca, Turnu Severin and Gloria Bistrita were the other clubs in danger.
Many of the clubs face considerable infrastructure difficulties and are struggling to meet administrative, legal and financial conditions laid down by UEFA.
Universitatea Craiova, one of Romania's top clubs, has been excluded from the top flight for this season after a labour dispute with a former coach.
Dragomir said he was concerned even for the top two teams in the country - league leaders Steaua Bucharest, who are playing in the Europa League, and champions CFR Cluj, who still have a slim chance of progressing to the Champions League knockout stages.
"I am concerned about Steaua and CFR, there are financial problems," he said. "I don't know how it will be resolved."