Germany's only black MP said this week he had received death threats from right-wing extremists days after finding holes probably made by a pellet gun in his constituency office window.

Karamba Diaby, a lawmaker for the centre-left Social Democratic Party (SPD), told German media that he had received the anonymous threat by email, which was reportedly signed with the words "Sieg Heil" and "Heil Hitler".

"I am taking the threat very seriously and have informed the police immediately," Diaby told the DPA news agency on Thursday.

"Investigations have been started without delay and measures have been taken to protect me."

The threat comes just days after Diaby tweeted a picture of three holes in his office window, which investigators believe were made by plastic pellets shot from an "airsoft" gun.

Regional newspaper Mitteldeutsche Zeitung said they had also received a copy of the threatening e-mail.

The newspaper reported that it was signed by a group calling themselves the "coup d'etat orchestra", and made reference to the recent killing of conservative politician Walter Luebcke.

Diaby, 58, was born in Senegal but moved to the former communist East Germany in the late 1980s to study chemistry.

In a 2017 interview with AFP, he recalled experiencing racism both before and after the fall of the Berlin Wall and German reunification in 1989-90, suffering a beating from neo-Nazis in 1991.

Elected in 2013, he represents a constituency in the eastern state of Saxony-Anhalt, a region where the far-right AfD party enjoys widespread support.

The threats against him come amid a growing wave of aggression towards politicians in Germany.

Last year, police recorded 1,241 politically motivated crimes against elected officials of all stripes.

Three mayors have resigned in recent months after death threats and attacks on their cars.

Another mayor has made headlines in recent days after applying for a licence to carry a weapon in self-defence.

Politicians from the conservative CDU and the Green Party have also received death threats from right-wing extremists in recent months.