In a letter to the kidnappers, a copy of which was sent to Aljazeera, the institute said: "If you are Muslims and believers of Islam you should know that to kidnap, hold under detention, haggle over and threaten with killing any person for any reason has been strictly forbidden by the Almighty Allah."
"Your deed is against Allah ... and means disobeying his commandments and disregarding the teachings and the sunnah (practice) of His messenger (peace be upon him) as well," stated the letter signed by Mohammed Salim Abdul Allah, senior director for the body.
Established in 1927, the Institute Islam-Archiv-Deutschland, is the oldest Muslim body in Germany.
Susanne Osthoff, a 43-year old convert to Islam, has been missing since 25 November. She had been working as an archeologist and was abducted along with her driver.
"Osthoff is a Muslimah and believer," said the letter, adding "as such she is our and your sister in belief.
"All of us have to protect and honour her with the utmost respect. You ought to recall and understand what this does imply."
The institute also pointed out in the letter that Osthoff is the mother of a young daughter.
Osthoff is seen in a video
released by her captors
"Can you imagine that your mothers or your wives are hostages instead of Mrs Osthoff?"
The letter continued: "Your deed is surely inhumane ... Do you really want to stand in front of Him on the day of judgement ashamed and guilty?"
In a final plea, the institute called on the captors to "beware ... and reverse this inhumane and awful action".
Fires of damnation
The letter further warned: "Set free Mrs Susanne Osthoff and her companion at once. Let the beloved mother return to her child.
"And remember, she came in peace to help and so her place in heaven is as sure as yours in the eternal fires of damnation, unless you stop now and help to undo the harm you have done already."
"Can you imagine that your mothers or your wives are hostages instead of Mrs Osthoff ... Let the beloved mother return to her child"
Letter to captors from the
Central Islamic Institute, Germany
Osthoff has been seen in a video released by her captors, who threatened to kill her and her driver if Germany does not stop cooperating with the US-backed government in Baghdad.
German Chancellor Angela Merkel on Sunday issued a joint appeal with other leading national figures for Osthoff's release after a reported deadline to meet the kidnappers' demands passed.
"The German government is doing everything it can to save the lives of Susanne Osthoff and her escort," Merkel wrote in the Bild am Sonntag newspaper.
"We call on the perpetrators to release the hostages immediately."