Officials have discovered that the dead body of Papadopoulos was not in his grave just before the first anniversary of his death.
The Greek Cypriot police have cordoned off the site of the robbery in the Deftera village cemetery and been searching the site.
Police investigators said that the motive was unclear.
Saturday is the first anniversary of the death of Papadopoulos, who was Cyprus' president from 2003 to 2008.
Investigators believe the body was taken either late Thursday night or early Friday morning. The motive is unclear.
Papadopoulos died a year ago on Saturday from lung cancer at age 74. He served as Greek Cypriot leader from 2003 until March 2008.