German police have arrested three Syrian nationals suspected of being sent to Germany by the militant group Islamic State, prosecutors said on Tuesday.

Federal prosecutors said they suspect the three men were dispatched to Germany in November 2015 "either to carry out a mission that they had been informed about or to wait for further instructions".

The three men, aged from 17 to 26, were arrested in the northern state of Schleswig-Holstein on Tuesday, according to a statement from the Federal Prosecutors headquarters in Karlsruhe. It was not immediately clear where any attack would have taken place.

"Concrete missions or orders have not so far been found in the course of investigations carried out," the prosecutors said after the trio was arrested by special forces with support from 200 federal and local police.

Authorities also searched the flats of the three suspects but had no further details on what they might have found.

Around a million migrants arrived in Germany last year, and concern about their presence has grown after a series of violent attacks, three of which were carried out by asylum seekers. Of those, two were claimed by Islamic State.

Those attacks in July put the country on edge and led to pressure on Chancellor Angela Merkel to introduce an upper limit of 200,000 refugees per year, as her Bavarian allies, the Christian Social Union, are demanding. She refuses any cap.

"Based on the information that the Federal Crime Office has so far been able to obtain, the three are strongly suspected of coming to Germany in November 2015 on orders from Islamic State," the federal prosecutors' office said.

It said a suspect identified as Mahir Al-H. became a member of Islamic State in September 2015 and received weapons and explosives training in Raqqa, the militant group's de facto capital in Syria.

In October, he and the two other suspects, Mohamed A. and Ibrahim M., signed up with an Islamic State official responsible for operations and attacks outside Islamic State territory and travelled to Europe, the prosecutors said.

"The three were supposed to fulfil an existing order (for an attack) or wait for further instructions," the prosecutors said.

Islamic State allegedly provide them with passports, more than $1,000 in cash and cell phones with a special communications program. The suspects travelled through Turkey and Greece before arriving in Germany in mid-November 2015, at the height of the migrant crisis.