The club, founded 111 years ago and crowned champions only two years ago, said in a statement on their official website that it was impossible for them to meet the requirements for the licence which would allow them to compete in the top flight.
Gyor have an estimated 150 million forint ($556,091) public debt, mainly due to the collapse of brokerage firm Quaestor, the club's main shareholder.
"We knew it would happen, but it is still so, so sad and disappointing," Vasile Miriuta, the former Hungarian international who now manages Gyor, was quoted as saying by Hungarian news agency MTI.
"We have still four games in the top flight, but what happens after that, surely we don't know."
Gyor, who finished runners-up in the league last season, have played a rich part in Hungarian football history, having won four league titles and lifted the domestic Cup four times too.
They have been in the top flight since 1961, with their greatest achievement having been to reach the semi-final of the European Cup in 1965.
($1 = 269.7400 forint)
(Reporting by Zoltan Fazekas; Editing by Ian Chadband)
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