Palestine Liberation Organisation second in command Saeb Erakat made the demand in a letter addressed to the president of the European Broadcasting Union, Jean-Paul Philippot.
"The Eurovision song contest this year will be held in Stockholm, Sweden, the first EU member state in Western Europe to officially recognise the State of Palestine," Erakat wrote.
"Your decision is totally biased and unacceptable.
"We call upon you to immediately revoke this shameful decision. It's also equally necessary for the European Broadcasting Union to apologise to Palestine and to millions of Palestinians around the world."
Organisers of the annual contest have already come under fire from Spain, which condemned a ban on the Basque regional flag.
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"It is a constitutional, legal and legitimate flag and the Spanish government will defend it whenever needed," Deputy Prime Minister Soraya Saenz de Santamaria said Friday.
Spanish Foreign Minister Jose Manuel Garcia-Margallo spoke to Madrid's ambassador in Sweden "so that he could immediately tell the organisation that it is a constitutional flag and cannot be in that list", a ministry spokeswoman has said.
Eurovision has apologised to Spain and blamed the publication by mistake of a draft version of its flag policy listing banned banners, including that of the Islamic State group.
Under Eurovision rules, regional flags or those belonging to federated states, or including commercial, religious or political messages, are all banned.
Those that are allowed are the flags of countries taking part in the contest and any other UN member state, as well as the EU flag and the rainbow banner that represents the LGBT movement.
Eurovision spokesman Dave Goodman told AFP that "the flag policy is not aimed against specific territories or organisations, and certainly does not compare them to each other".