Pakistan's Inter-Services Intelligence (ISI) agency was able to intercept emails between the German Police Project Team (GPPT), which has 180 officers in Afghanistan, and Berlin, according to the newspaper.
The Taliban even knew about German president Christian Wulff's surprise visit to Afghanistan two weeks ago, even though it was only announced publicly after he landed in Kabul.
"We have opened the door to the enemy," one unnamed German government official said.
The security breach was discovered by German intelligence agency BND during a computer update.
Pakistan denied the accusation to the Reuters news service.
However, Germany's Interior Ministry told English-language news website The Local that there were indications of Pakistani espionage that could not be confirmed and added that the computers in question were replaced with new ones featuring advanced security software.