The German-language message demanding an untraceable payment in the virtual currency was addressed to the parcel delivery service DHL, Bild daily reported.
The bomb, containing explosive powder from Polish fireworks, nails and screws, was received by a pharmacy adjacent to the Christmas market last Friday.
Bild reported that it included a battery-powered trigger device, and that the package made a hissing sound when it was opened but failed to detonate.
Police, on high alert one year after a jihadist attack on a Berlin Christmas market killed 12 people, quickly cleared the festive market in the city of Potsdam near the capital.
Police are searching for one or more suspects in Berlin or its surrounding Brandenburg state, after a DHL parcel believed to have come from the same source caught fire last month when it was opened in another city in the same eastern region.
The blackmailers have threatened to send more parcels in the pre-Christmas season unless DHL pays, police warned last week, calling on Germans to remain vigilant and to advise caution when accepting parcels.
Meanwhile a building in Ulm, Baden-Württemberg, was evacuated on Wednesday morning due to a suspicious parcel with an unknown sender, according to German media. A fence closing off a large area around the building has since been set up.
"As long as we don't know what is in the package, we have arranged for the fence to allow us to conduct our investigation," said a police spokesperson.
Some roads in the city centre of Ulm have also been closed off.