It cited the chief public prosecutor in the northern town of Celle as saying on Friday that arrest warrants had been issued for the two men and one woman suspected of helping to prepare a serious act of violence against the state.
The prosecutor's office was not immediately available for comment when contacted by Reuters.
German authorities have been on high alert since December, when an Islamist truck attack on a Berlin Christmas market killed 12 people.
Leading soccer team Borussia Dortmund's bus was attacked with explosives on Tuesday, injuring defender Marc Bartra. Three identical letters printed in German found near the scene suggested a possible Islamist motive.
There was no suggestion in the Focus report that the three suspects arrested were linked to either the Berlin or the Dortmund attacks.
The magazine said the trio - a 27-year-old Afghan, a 27-year-old Turk and a 25-year-old German - were arrested on Thursday evening in three different German cities and were in custody.
It said they were suspected of supporting a German member of an ultra-conservative branch of Islam who police arrested in February. That man admitted planning to lure police or soldiers into a trap and kill them with a home-made bomb.