News channel N24 on Tuesday identified the hostage as 43-year-old Susanne Osthoff from the southern state of Bavaria.
The news of her abduction came on a day when two Iranian women, seized in Iraq with four Iranian men on Monday near Balad, north of Baghdad, were released unharmed by the captors.
Osthoff's mother told the channel her daughter had been organising aid shipments for Iraq. She said she was counting on the German government to help rescue her daughter.
ARD public television said Osthoff, an archaeologist by profession, and her driver had been taken hostage. It described her as having been active in Iraq for several years and fluent in Arabic.
Osthoff's kidnappers had, in a video tape handed to ARD in Baghdad, threatened to kill her and her driver unless Berlin stopped cooperating with the US-backed Iraqi government, ARD said.
The channel added that a "very short time limit" was given.
Extracts from the tape on ARD's website showed two people sitting on the ground with their eyes covered by white material surrounded by three masked, armed figures, one of whom appeared to be reading from a piece of paper.
German Foreign Ministry spokesman Martin Jaeger, travelling with Foreign Minister Frank-Walter Steinmeier said in Washington Osthoff had been missing since Friday and that a unit had been set up to secure her safety.
He added: "The German government is directing its efforts to bringing her to safety as soon as possible."
Susanne Osthoff has been
missing since Friday
New German Chancellor Angela Merkel will meet her cabinet on Tuesday to discuss the case, a government spokesman said.
Germany opposed the US-led war in Iraq and has ruled out sending troops.
But Merkel wants to improve relations with the US and said earlier this month Berlin would carry on with the previous government's policy of helping to train Iraqi forces outside Iraq.
Also on Tuesday, Christian Peacemaker Teams confirmed that four people from the group have been missing since Saturday.
"On 26 November 2005, two members of Christian Peacemaker Teams (CPT) and two members of a CPT visiting delegation were taken in Baghdad," the statement said.
A joint US-Iraqi regional military coordination centre said on Tuesday that two Iranian women seized with four other Iranian pilgrims near Balad a day earlier, had been freed.
The Iranians were seized along with their Iraqi guide and driver by armed men who held up their minibus late on Monday.The driver was wounded, witnesses reported.
Iraq was rocked by a wave of foreigner abductions and beheadings in 2004 and early 2005. But since May, abductions have dropped off considerably, mainly because many Western groups left Iraq and security precautions for those remaining have been tightened.
Attackers in several cars shot dead an influential Sunni Muslim scholar outside his mosque in the city of Falluja on Tuesday, witnesses said.
Hamza Abbas al-Issawi, a mufti or senior Islamic authority, was coming out of the Wihda mosque after evening prayers when gunmen pulled up near him and opened fire.
Witnesses said the cleric was
well-known in Falluja
"It is shocking, everyone in Falluja knows him, he is very respected," said Safah Naji, a witness.
"Even all the insurgents know him and everyone liked him."
Falluja is a former stronghold of the insurgency and is overwhelmingly Sunni Arab.
The attack follows the killing of other senior Sunni Arab leaders in the past two days. Politicians Iyad Alizi and Ali Hussein, members of the Iraqi Islamic Party, were shot dead as they drove through Baghdad on Monday.