The body-snatching horrified people in Cyprus and came as the island's Greek and Turkish Cypriot leaders are locked in complex reunification talks that have made limited progress.
Police said the tomb raiders struck late Thursday or early Friday. There was no immediate indication of a motive.
Police spokesman Michalis Katsounotos said three people were initially detained for questioning but released without charge. He gave no more details.
President Demetris Christofias, who beat Papadopoulos in March 2008 elections, urged Cypriots "to remain calm in the face of this provocative act."
"This is an unacceptable, unholy, unethical and condemnable act that damages our tradition, our culture and our respect toward the dead," Christofias said.
Papadopoulos is seen by some nationalist Greek Cypriots as a symbol of resistance against peace deals they believe have been weighted against them.
"What happened is 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," said Andros Kyprianou, the head of Cyprus' ruling AKEL party. He urged that those responsible be "caught and made an example of."
Mounds of fresh earth were piled by the fenced-off grave site Friday at the Deftera Village Cemetery as about 80 police and two pathologists combed the area and nearly fields for clues.
The robbers had removed a heavy marble plaque from on top of the grave, police said, digging down to the coffin and taking the body of Papadopoulos, who died of lung cancer on Dec. 12, 2008, at 74.
A light-grey substance was sprayed across the tombstone in a southwestern suburb of the capital Nicosia, obscuring Papadopoulos' name and date of birth but leaving the tombstone otherwise unharmed. Local media said the substance appeared to be lime, possibly used to erase the robbers' shoe prints.
The violated grave was discovered by one of Papadopoulos' former security guards when he went to make arrangements Friday morning for a ceremony marking the anniversary of the former president's death, police said.
The island was split in 1974 into a Turkish-occupied north and an internationally recognized Greek Cypriot south after Turkey invaded in response to a coup by those wanting to unify the island with Greece.
A British-trained lawyer, Papadopoulos was a guerrilla leader for the Greek Cypriot group EOKA, which waged an anti-colonial campaign. Later, at 26, he served as the youngest cabinet minister in the island's first post-independence government.
In 2004, he urged Greek Cypriots to reject a U.N.-brokered reunification plan, which he vilified as entrenching the island's division rather than ending it. Three-quarters of Cypriots obliged him in an April 2004 referendum. Two-thirds of Turkish Cypriots accepted the plan.
Papadopoulos' family issued a statement saying they were grieved and angered by the "sacrilegious act."
The theft of his remains "cannot in any way bury the policy or erase the political will of Tassos Papadopoulos. Wherever his body may be, his voice will still be heard," the family statement said.
Relatives, former colleagues and politicians visited the desecrated site throughout the day, with Papadopoulos' daughter, Anastasia, taking away a framed photograph of her father that had stood at the grave.
The body snatching was roundly condemned, including by the European Union's Swedish presidency and Greek Prime Minister George Papandreou.
"This is really shocking. I cannot believe that such a thing could happen, especially in Cyprus," said Andros Christou, a nearby resident. "The only thing that I heard last night was rain and thunder."