About 90 people were slightly injured during pro-Puigdemont protests in Barcelona on Sunday, including 22 police officers.
Spain has to clarify its legal case against Puigdemont, after which German courts will have to decide if the accusations are sufficient to justify extradition.
"The competent district court is deciding whether Mr. Puigdemont will be provisionally detained", state prosecutor Ralph Doepper said.
Her spokesman insisted Monday that the decision on Puigdemont's extradition rested exclusively in the hands of the German regional justice authorities.
The ruling must normally be made within 60 days under German law.
Spain's Deputy Prime Minister Soraya Saenz de Santamaria welcomed the arrest as "good news", saying: "No one can make a mockery of the courts forever".
However protesters in Barcelona saw the move as a provocation.
After meeting with independence parties, Roger Torrent, the Catalan speaker, tabled a special session for tomorrow morning to plot a path to an inauguration.
"I have no doubt that Catalan society will act as it always has, with non-violence", he said.
Spain charges exiled Puigdemont and 12 Catalan leaders with rebellion
Several separatist leaders, including former Catalan vice president Oriol Junqueras, have been in custody since past year . The leaders are charged with rebellion, along with eight others, over their involvement in a push for independence.
Spain was plunged into its worst political crisis in four decades when Puigdemont's government flouted a court ban and held an ad hoc referendum on independence for the northeastern region in October.
The court said they would be prosecuted for "rebellion", a charge which carries a maximum sentence of 30 years in prison.
Puigdemont's lawyer, Jaume Alonso-Cuevillas, has argued that the rebellion charges in Spain would be punishable in Germany only if conducted through violent means, and that Puigdemont was never violent.
He travelled to Finland last week to speak at an event but left on Saturday to return to Belgium, only to be seized by German police after crossing the border from Denmark in an operation involving Spanish intelligence agents.
The vote had been swiftly followed by the Catalan parliament's declaration of independence on October 27.
Puigdemont was detained by German police in the north of the country, following a request by the Spanish police. Since then, new elections in Catalonia have yielded another government backing separatism, though it has not been able to name a president since so many leaders of the separatist cause, like Puigdemont, face trial.
Elsa Artadi, a lawmaker with Puigdemont's Together for Catalonia party, said that he should fight his extradition.
Carles Puigdemont, the former president of Catalonia, is set to spend Easter in a jail in northern Germany.