The Israeli government on Sunday said it was "shocked" by an anti-Semitic tweet sent to an Israeli football player during a second division game in Berlin, in an incident being investigated by German police.

In a profanity-laced insult, an apparent fan of FC Union Berlin tweeted that Almog Cohen, captain of opposing team Ingolstadt, should disappear into "the chamber", a reference to the gas chambers used by the Nazis to kill Jews during the Holocaust.

The tweet was posted after Cohen received a red card during Friday's match in the German capital, which Union Berlin won 2-0.

"We are shocked by the anti-Semitic tweet against Almog Cohen and expect the German authorities to take firm action against the person" responsible, foreign ministry spokesman Emmanuel Nahshon told AFP.

Both football clubs immediately condemned the abuse, with Union Berlin swiftly filing a complaint with police for incitement to hatred.

"I'm ashamed of such Union fans," club president Dirk Zingler said in a statement. "FC Union stands for humanistic and democratic values. Anyone who doesn't share these values has no place in our club or our stadium."

A Berlin police spokeswoman told DPA news agency that the state security service, which deals with politically motivated crimes, had opened an investigation.

The rant brought an outpouring of support for 30-year-old Cohen, who also plays for the Israeli national team.

"Almog, you will never be alone!", tweeted the Israeli ambassador to Germany, Jeremy Issacharoff, condemning the "despicable" anti-Jewish insult.

Christoph Heubner, vice-president of the International Auschwitz Committee, said the hate-filled tweet highlighted a worrying rise in anti-Semitism in Germany.

Such "outbursts of hatred" are "disgusting and alarming -- and not just to Holocaust survivors -- because of their direct reference to the gas chambers of Auschwitz," he said.

Cohen, who has lived in Germany for nine years, tweeted a message of thanks to his supporters.

"As a Jewish professional football player in Germany I just want to say: I am very proud of my heritage and of representing my country in the second division and being captain of Ingolstadt 04," he wrote.

"A big thank you to my club which gives me the support and therefore the strength to master any situation."

The German Football Association (DFB) also slammed the "disgusting" tweet and said it would look into the matter.

The DFB is no stranger to condemning racist behaviour from fans, especially from hardcore so-called "Ultras" linked to the far-right.

In a separate incident at the weekend, fourth-tier club Chemnitzer FC sparked an uproar after it allowed supporters to stage a tribute to a recently deceased fan, who was reportedly a known neo-Nazi, at the start of a regional match.

The deceased, Thomas Haller, for years provided security for the club and co-founded the "HooNaRa" (Hooligans-Nazis-Racists) group in the 1990s that was disbanded in 2007, local broadcaster MDR reported.

He remained a leading figure in Chemnitz's far-right scene, MDR said, and took part in racist riots that rocked the city last year following the fatal stabbing of a German man, allegedly by immigrant men.

Some of the protesters at the time were arrested for giving the Hitler salute, which is illegal in Germany.

On Sunday, the club announced their CEO and commercial managing director Thomas Uhlig had resigned with immediate effect over the scandal.

Chemnitz also fined striker Daniel Frahn, who held up a T-Shirt, which is popular amongst neo-Nazis, during the match but later apologised.

"I was not aware that this T-shirt was so widely used in the Nazi scene," said Frahn in a statement.

The latest controversies come less than a month after the German government revealed a startling increase in anti-Semitic hate crimes, echoing a trend seen in other Western countries like France as the political climate becomes more polarised and the far-right more outspoken.

German police recorded 1,646 offences motivated by hatred against Jews last year, an increase of almost 10 percent and the highest level in a decade.

Among these were 62 violent offences, up from 37 in 2017.

Most of the crimes were committed by far-right sympathisers, but Berlin has also expressed growing concern about anti-Jewish sentiment among migrants from Arab states.

"It shames and hurts me that anti-Semitism is once again showing its ugly face more often and more openly in Germany, of all places," German President Frank-Walter Steinmeier said on Sunday.