The veteran anti-whaling campaigner, a Canadian national, was detained in Frankfurt on Sunday on charges stemming from a high seas confrontation over shark finning in 2002.
He is accused of having "put a ship's crew in danger" in the incident, a Frankfurt prosecutor said.
Watson's lawyer Oliver Wallasch said that after a hearing Monday that his client must remain in custody until the Costa Rican extradition request is considered, adding that he did not know how long the process would take.
"My client is shocked," Wallasch said.
A media report in Australia, citing Costa Rican reports, said he also faced an outstanding warrant for attempted murder during the same incident.
"The German police have said that the warrant for Captain Watson's arrest is in response to an alleged violation of ships traffic in Costa Rica, which occurred during the filming of 'Sharkwater' in 2002," Sea Shepherd said.
The specific "violation of ships traffic" incident took place in Guatemalan waters when Sea Shepherd encountered an illegal shark finning operation, run by a Costa Rican ship called the Varadero, it added in a statement.
"On order of the Guatemalan authorities, Sea Shepherd instructed the crew of the Varadero to cease their shark finning activities and head back to port to be prosecuted," the group said.
It claimed that while escorting the Varadero back to port, the tables were turned and a Guatemalan gunboat was dispatched to intercept the Sea Shepherd crew.
"The crew of the Varadero accused the Sea Shepherds of trying to kill them, while the video evidence proves this to be a fallacy," said the group, which was set up in 1977 to campaign against the slaughter of ocean wildlife.
"To avoid the Guatemalan gunboat, Sea Shepherd then set sail for Costa Rica, where they uncovered even more illegal shark finning activities in the form of dried shark fins by the thousands on the roofs of industrial buildings."
Watson was being assisted while in prison by members of the European Parliament Daniel Cohn-Bendit and Jose Bove, Sea Shepherd added.
Our hope is that these two honourable gentlemen can set Captain Watson free before this nonsense goes any further," the group said.
Sea Shepherd is best known for its annual pursuit of the Japanese whaling fleet in Antarctica, using increasingly militant ways to halt the hunt.
This year, after setting off from Australia, the group hurled stink bombs at the boats on the high seas and used ropes to try to tangle their propellers in a series of exchanges which saw the whalers retaliate with water cannon.
The whaling fleet killed less than a third of the animals it planned to because of the sabotage attempts.