Bashari did not provide any further details about the police operation which took place not far from the area where the woman went missing.
Police have also not given any details of the kidnappers or any group they may belong to.
The German foreign ministry in Berlin confirmed the aid worker had been rescued.
“She is in the safety of the German embassy,” a ministry spokesperson said.
On Sunday a videotape showing the kidnapped German aid worker was shown on Tollo TV, a private Afghan television channel.
The woman in the video, who identified herself as “Christina Meier”, was shown sitting on the floor with her head covered by a white scarf.
“I’m ok, I want my country to try to help secure my freedom as soon as possible,” she said, reading haltingly in the local Dari language and prompted by a man nearby.
She said she worked for the charity ORA International.
The man, who had his face covered, then demanded the release of “innocent prisoners” in exchange for the aid worker’s freedom.
The man said that he was a member of “a special group” that was not the Taliban.
Hamid Karzai, the Afghan president, had condemned the kidnapping and video as “a criminal act and an un-Afghan act”.
The woman was abducted from a restaurant in Kabul on Saturday, Afghan officials said.
Ulf Baumann, a spokesman for ORA International, said the 31-year-old Meier and her husband, also a German, had been working for the organisation in Kabul since September 2006, but he did not disclose the names of the woman or her husband.
The abduction of the woman had threatened to create a third hostage crisis involving foreigners for the Afghan authorities, who were already battling to secure the freedom of the 19 Korean aid workers and a German engineer captured last month.
Two German engineers were seized about a month ago in the southern province of Wardak by the Taliban.
One of the engineers was shot shortly afterwards and their captors have threatened to kill the other if Germany does not withdraw its troops from Afghanistan.
Germany is involved in training Afghan security forces, has contributed some 3,000 troops to the Nato-led International Security and Assistance Force and has six Tornado reconnaissance planes helping to spot Taliban positions.