Mr Bekesi said that he decided to go because of disagreements with the Prime Minister, Gyula Horn, over the pace and scale of economic reform, in particular, of Hungary's privatisation programme.
His departure triggered speculation about a split in the ruling coalition between Mr Horn's Socialists and the more pro-free market Alliance of Free Democrats (AFD).
It also prompted predictions of back-pedalling over economic reform and a sharp decline in interest among potential foreign investors.
"There is a real danger that the way [foreigners] view Hungary will be hurt, because the resignation is not just simply of a minister but of the man whose name has been synonymous with the government's economic policy," said Ivan Peto, the AFD president.
When the AFD, the junior partner in the coalition, agreed to go into government with the Socialists last June, one of its demands was for the appointment of Mr Bekesi as Finance Minister. Although he is a member of the Socialist party, Mr Bekesi was known for his pro-market stance. Many Socialists used his presence in the cabinet as proof that they had distanced themselves from the party's Communist past.
During his time in office, Mr Bekesi devised an austerity programme that called for cutbacks in public spending and an acceleration of privatisation.
The programme won him praise from the World Bank and the International Monetary Fund but brought him into increasing conflict with the interventionist policies of Mr Horn.
The tension between the two men burst into the open last month, when Mr Horn blocked a proposed sale of 14 state-owned hotels to the American General Hospitality group. The Prime Minister complained that the price that had been agreed by a privatisation commissioner working under Mr Bekesi was too low.
At the time, Mr Horn said that the process of privatisation was not serving the interests of the country and needed to be "supervised more closely".
Mr Bekesi immediately accused him of "political intervention" and of trying to "deter market conditions". He said that this would deter potential investors.
Earlier this month Mr Horn, whose political career was built within Hungary's former ruling Communist Party, dismissed the privatisation commissioner, Ferenc Bartha. He then announced his intention to appoint a privatisation minister, effectively removing it from the control of Mr Bekesi.
While Mr Horn says that he is committed to further privatisation, political observers say that he has been swayed by trade unionists' worries about the social costs of the process and wants it to proceed more gradually and entail fewer job cuts and pricerises.
Many of Hungary's former state-owned agricultural, industrial and trading concerns have been sold off since Communist rule came to an end in 1989. But there are still many big firms, including public utilities and banks, which have not been privatised.Reuse content