She said in an open letter Friday, "Exile will be a tough road, but it is the only way I have to recover my political voice".
"The sole objective of this appearance is to verify the identity of the person arrested", the regional tribunal in the town of Schleswig said in a statement.
"This Europe is shameful!", they chanted outside of the European Commission offices.
Catalan police blocked the street and issued a call for people not to gather.
The former Catalan regional president was at the time of his detention heading to Belgium, according to Puigdemont's spokesman Joan Maria Pique. Protesters also turned out in the northern city of Girona, where Puigdemont was mayor before he became regional president in 2016.
Puigdemont's detention puts his fate in the hands of German courts, which will have to decide whether to pass him to Spanish authorities to face charges of "rebellion and misuse of public funds".
Under the rules of the EWA, active since 2004, a court in one European Union member state can only extradite a person sought by another member state if they are confident the suspect will face equivalent fair legal procedures and trial.
Spain was plunged into its worst political crisis in three decades when Puigdemont's government flouted a court ban and held an ad-hoc referendum on independence for the northeastern region in October.
Aside from the scenes in Barcelona, the arrest of the fugitive ex-leader of secession-minded Catalonia has sparked mixed reactions in Spain.
Like Puigdemont, other politicians facing charges have left Spain to live in self-exile.
Puidgemont's arrest follows fresh legal action against separatist politicians from the wealthy northeastern region and it is coming after a Spanish High Court detained five Catalan politicians for their role in the region's secessionist bid staged in October a year ago.
-By Joseph Wilson in Barcelona.
Separatist parties have abandoned plans to name a new president following the candidate's arrest, and if a new president is not elected by May 22, new elections will be automatically triggered.
National news agency DPA quoting unnamed sources said Puigdemont was driven in a small van with tinted windows to a prison at Neumuenster.
He is being held by German police on a Spanish arrest warrant after trying to cross into Germany from Denmark.
Puigdemont had been wanted in Spain since leading a parliamentary session in October a year ago that saw separatist lawmakers vote for the region of Catalonia to declare independence from Spain.
It is not clear if Puigdemont will be immediately extradited from Germany. "We received a very hard blow yesterday. butut we must pick ourselves up quickly to build a future for all".
"We simply had the information that he was supposed to be in Germany or had entered the country", he said.
It said in a statement that "the question of whether Mr. Puigdemont has to be taken into extradition custody will then have to be determined by the higher regional court in Schleswig".
A Spanish Supreme Court judge charged 13 Catalan separatist politicians with rebellion Friday for their attempts to make the region independent of Spain, dealing a heavy blow to the secessionist movement. German police say Puigdemont has been detained on a European arrest warrant. But his lawyer, Jaume Alonso-Cuevillas, said yesterday that Puigdemont had left Finland and was en route to Belgium. He says Puigdemont is at a police station. Separatists won that vote, and Puigdemont's government declared independence. Spain has also issued five warrants for other separatist who fled the country.