The ruling, a blow to Europe's post-September 11 counter-terrorism plans, upheld an appeal by al-Qaida suspect Mamoun Darkazanli, a German-Syrian dual national whom Spanish authorities accuse of providing the network with logistical and financial support.
The Federal Constitutional Court in Karlsruhe ruled that the European warrant violated the German constitution and the suspect's basic rights, and was thus invalid in Germany.
"He must be set free following this verdict, which is a blow for the government in its efforts and fight against terrorism," German Justice Minister Brigitte Zypries said.
Darkazanli, 46, appears in a 1999 wedding video with two of the three suspected pilots of the 11 September 2001 attacks on the US - Marwan al-Shehhi and Ziad Jarrah - who lived and studied in Hamburg along with suspected lead hijacker Mohamed Atta.
Darkazanli has never been charged in Germany, whose constitution prohibits the extradition of its own citizens for trial.
He was taken into custody in October at Spain's request, and his case was seen as a test of the new European arrest warrant - a system meant to allow the swift cross-border handover of terrorist suspects - which came into force in Germany in August.
EU spokesman Martin Selmayr said the arrest warrant would survive the German court ruling.
He said the ruling did not declare the European arrest warrant unconstitutional, but merely the German national law which implements it.
Null and void
"From a first reading, it's a judgment that declares null and void the German implementation law, not the European arrest warrant," Selmayr said in Brussels.
"He must be set free following this verdict, which is a blow for the government in its efforts and fight against terrorism"
German justice minister
He added that the court in Karlsruhe said the German law did not make full use of provisions to protect suspects' rights under the European directive setting up the arrest warrant.
Selmayr said the court's ruling was a blow to European anti-terrorist plans in the short term because the warrant will not apply in Germany until a new national law on implementing it is introduced.
However, he said in the longer term, the ruling could strengthen the warrant by making clear the protection offered to suspects' rights.
Darkazanli is among 41 suspects, including Osama bin Laden, indicted by Spanish Judge Baltasar Garzon, who has been investigating al-Qaida.
He faces up to 12 years in a Spanish prison if convicted of membership in a "terrorist organisation".
The United States has labelled Darkazanli's Hamburg-based trading company a front for "terrorism". He appeared on a US suspects lists after September 11 but has denied any links to bin Laden or the attacks.
German police questioned him shortly after September 11, but he was freed for lack of evidence and continued to live in Hamburg.