Atef Adwan, the minister of refugee affairs, came to Germany after a visit to Sweden, the source said, despite a European Union policy of no contact with the radical movement.
The source could not say how long Adwan had stayed or whom he had met with in Germany.
Adwan told AFP in Stockholm on May 9 that he planned to visit four European countries under the so-called Schengen accord, which states that a visa delivered by any member country is valid for all the others.
He did not state which nations he planned to visit before his visa expired
Adwan arrived in Sweden May 6 to attend a conference on Palestinian exiles before traveling to Norway.
He met with Norwegian deputies and an official from the foreign ministry in Oslo and on Monday issued an appeal in the Norwegian capital for restoring humanitarian aid to the Palestinians.
Adwan’s visit to Scandinavia came in the face of protests from Israel and France for granting legitimacy to a movement they view as a terrorist organization.
As a member of the European Union, Germany shares the same concerns.
“The (German) government rejects any contact with members of the Hamas-led government because the organization does not fulfill the three criteria set by the European Union,” a German foreign ministry spokeswoman told AFP.
“Mr Adwan is not welcome in Germany.”
The EU has insisted that Hamas recognize Israel, respect accords signed by the Israelis and the Palestinians and renounce violence. It suspended direct aid to the government in the face of its refusal to respect these terms.
Berlin had reportedly asked the Norwegian government to tell Adwan that he was considered persona non grata in Germany.