The German ambassador was summoned to a meeting with officials in Ankara after German television broadcast a satirical song about Turkey's President Recep Tayyip Erdogan.
Shown on public broadcaster NDR, the two-minute song entitled Erdowie, Erdowo, Erdogan, features footage of Erdogan and Turkish riot police battling protesters.
Its lyrics criticise recent crackdowns on the free press by the Turkish government. "A journalist that writes something that doesn't suit Erdogan is in jail tomorrow," it says.
Days after the song's broadcast on 17 March, Germany's ambassador to Turkey, Martin Erdmann, was summoned by Turkey's Foreign Ministry to explain "in length" the reason for the broadcast, Spiegel reported.
The spat comes amid attempts by German Chancellor Angela Merkel to reach an agreement with Erdogan in an attempt to ease the flow of refugees and migrants that have travelled to Europe from Turkey.
Prosecutors have opened more than 2,000 cases against those accused of criticising Erdogan since he became president 18 months ago. Those investigated include academics, journalists, a 13-year-old boy and World Cup star Hakan Sukur.