German police have arrested a doctor in Berlin suspected of convincing a young man to join Islamic State in Iraq, where he carried out a suicide bombing on behalf of the insurgents, prosecutors said.

The 24-year-old recruit, who was described in a statement as "mentally unfit", travelled to Islamic State-controlled territory in 2014 and killed at least 12 Iraqi soldiers in a suicide bombing in the city of Baiji in May last year.

A spokesman for the prosecutor's office in Karlsruhe said that the bomber's parents were both migrants to Germany, but declined to say where they were originally from. The doctor had an Arab father and German mother.

Investigators confiscated a gun sight, mobile phones, electronic memory devices and documents found in the doctor's Berlin apartment.