Germany's anti-Semitism commissioner, Felix Klein, has urged authorities to stop protesters using the Nazis' yellow star forced on Jews in World War Two.
Some protesters have replaced the word "Jude" (Jew) with the phrase "ungeimpft" (unvaccinated), equating Covid restrictions with the persecution of Europe's Jewish population.
The yellow Star of David has also been seen in protests in London.
Mr Klein said he hoped German cities would follow Munich in banning it.
"If people pin so-called Jewish stars on themselves in demonstrations, thereby drawing comparisons that relativise the Holocaust, then the means provided by law should be applied against them," he told Tagesspiegel newspaper.
The Nazis made wearing the yellow Star of David badge mandatory throughout territories they occupied, dehumanising Jews by marking them out as different. Anyone found without one faced a fine, prison or death.
Anti-lockdown protesters argue that the ruling liberal establishment is violating their personal freedom and exaggerating the Covid health risks. However, the head of the Central Council of Jews in Germany, Josef Schuster, said last year it was "unspeakable" that Germans were comparing restrictions on their lives with the abuses of the Third Reich.
The yellow star has appeared at protests beyond Germany too. British comedian David Baddiel drew attention to its use in London last month, and it was condemned by the Auschwitz Museum.
Instrumentalization of the tragedy of Jews who suffered, were humiliated, marked with a yellow star, and finally isolated in ghettos and murdered during the Holocaust, in order to argue against vaccination that saves human lives is a sad symptom of moral and intellectual decline.— Auschwitz Memorial (@AuschwitzMuseum) April 24, 2021
The head of the UK-based Centre for Countering Digital Hate, Imran Ahmed, said anti-vaxxers in particular had "instrumentalised" anti-Semitism as it had given them new audiences, and he was angered by the use of the yellow Star of David.
"I cannot think of many things more disgusting than comparing vaccines that will save countless lives to the industrial slaughter of Jews in the Holocaust," he told the BBC.
When the yellow star appeared in January at an anti-lockdown protest in the Czech capital, Prague, the Israeli ambassador condemned it as an insult to the millions murdered by the Nazis in the Holocaust.
Anti-Semitic offences in Germany rose to 2,300 last year, which the government's commissioner said was frightening but unsurprising, as in times of crisis people were more open to "irrational explanations, including anti-Semitic stereotypes".
He said they were espoused by the far right, conspiracy theorists as well as by the left.
It is not just the yellow star that has appeared at German protests. Far-right regalia and Imperial War Flags have been used during rallies close to the Reichstag parliament building.
Last month, the domestic BfV intelligence agency said some parts of the anti-lockdown movement were being placed under observation amid fears they were trying to undermine the state. It highlighted parts of the "Querdenker" (lateral thinkers) movement, which has drawn from the far-right AfD party, anti-vaxxers and conspiracy theorists.
Although not all Covid protesters were anti-Semitic, Mr Klein warned that diverse groups were finding common cause and anti-Semitism was the "cement that binds them together".
In a separate development, German intelligence said it was extending surveillance of an Islamophobic protest group in the eastern state of Saxony. It said Pegida had become "extremist" and "anti-constitutional" and was acting as a hinge between extremists and non-extremists.