The Bild am Sonntag said that a box packed with 340 grammes of cocaine valued at €40,000 were seized at the international airport in the eastern city of Leipzig in January.
The narcotics, posted from an unnamed South American country, were in liquid form and had been poured into the condoms and placed in the package addressed to the main postal centre at the Vatican.
The newspaper, citing a German customs report, said authorities handed the package with the drugs to a police officer at the Vatican with the aim of laying a trap for a culprit who might try to claim it.
But Bild said the parcel had remained there since January.
German investigators believe the intended recipient, who remains unknown, was likely tipped off that the package had been intercepted, the newspaper said.
The Vatican office of Interpol is now working on the investigation with German police, according to the report.
German customs authorities could not immediately be reached for comment.