The decision of the district court is expected on Monday.
The Schleswig prosecutor's office 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".
Catalan police have blocked the street and issued a call for people not to gather.
Outside of the German consulate demonstrators held up a photo of German Chancellor Angela Merkel sporting a Hitler-style moustache.
Mr Puigdemont's lawyer said on Saturday that the former president had slipped out of Finland.
Grassroots groups both for and against Catalan secession have called for protests later on Sunday in Barcelona.
Issuing an worldwide arrest warrant for Puigdemont on Friday, Judge Pablo Llarena accused the ousted Catalan leader of organising an independence referendum in October past year despite a ban from Madrid and "grave risk of violent incidents".
Thousands of pro-independence protesters were participating in a massive demonstration in the center of the Spanish city, carrying Catalonian flags and banners with slogans emblazoned across them, state media outlet RTVE reported on its website.
Catalan Parliamentary President Roger Torrent pledged to defy the central government in Madrid. Their detention sparked protests across Catalonia.
Spain had originally asked for Puigdemont's extradition from Belgium after he fled there in October, but later withdrew the request until Spanish Supreme Court judge Pablo Llarena concluded his investigation this week.
A Spanish police official told The Associated Press on customary condition of anonymity that Spain's National Center for Intelligence and police agents from its worldwide cooperation division helped German police in the capture of Carles Puigdemont.
The Catalan leader has been living in self-imposed exile in Belgium since he fled Spain five months ago amid the uproar over the referendum.
The arrest puts the fate of Puigdemont in the hands of German courts, which would have to decide whether to hand him over to Spanish authorities to face charges of "rebellion and misuse of public funds".
-By Joseph Wilson in Barcelona.
It is not clear if Puigdemont will be immediately extradited from Germany.
Puigdemont was stopped near the Danish border with Germany, a spokesperson of his party said on Sunday.
Police in the northern state of Schleswig-Holstein said highway police detained Puigdemont Sunday at 11:19 a.m. (0919 GMT; 4:19 a.m. EDT) near the A7 highway which leads from Denmark into Germany. "We received a very hard blow yesterday. butut we must pick ourselves up quickly to build a future for all". "They want to decapitate us but we are two million", she added.
Puigdemont's lawyer announced the arrest on Twitter and said his client had been taken to a police station.
Spain's Supreme Court ruled on Friday that 25 Catalan leaders would be tried for rebellion, embezzlement or disobeying the state.
A Spanish police official told The Associated Press under customary condition of anonymity that Spain's National Center for Intelligence and police agents from its global cooperation division helped German police to locate Puigdemont.