Grave robbers steal former Cyprus president's corpse
Mr Papadopoulos' body was removed after his grave in Nicosia was broken into overnight, officials said.
Mr Papadopoulos died of lung cancer in Nicosia in 2008, aged 74.
The theft from the Deftera village cemetery in Nicosia was discovered a day before the first anniversary of his death.
The desecration was discovered by one of Mr Papadopoulos's former guards who lights a candle in the cemetery every morning, the official Cyprus News Agency reports.
Eloquence and anger
The theft has been widely condemned. Marios Garoyan, leader of the former president's centre-right Diko party, condemned the act as a "heinous and terrible crime", AFP reported.
Andros Kyprianou, the head of Cyprus' ruling Akel party, described it as "macabre and utterly condemnable".
"I am honestly still trying to comprehend what kind of warped minds could even think of doing such a thing, let alone actually carry it out," he said.
Kypros Chrysostomides, who served as justice minister under Papadopoulos, said "such barbarous acts only do damage to Cyprus".
The motive for the theft remains unclear, investigators say. But it is bound to stir up passions over a UN-led peace effort aimed at reuniting the Turkish and Greek parts of the island, says the BBC's Malcolm Brabant in Athens.
Mr Papadopoulos was vehemently opposed to the peace plan, and his eloquence and anger convinced a resounding majority of Greek Cypriots to vote against it in a referendum, while Turkish Cypriots voted overwhelmingly in favour.
A veteran of Greek Cypriot politics, he became president in 2003 but lost a bid for a second term in 2008. He was defeated by Demetris Christofias, a former coalition partner.
One of the former president's achievements was to oversee the Republic of Cyprus's entry into the European Union in 2004.