Ahead of last week's UEFA Conference League meeting, Hajduk Split fans marched through the coastal town chanting: "Crush the Jews", "Rise up Adolf (Hitler)" and "Let's go Ustasha", referring to the country's World War II pro-Nazi regime, according to local media footage and reports.
Croatia's leaders, opposition parties, rights groups as well as the Jewish community strongly condemned the incident, while Israel's embassy in Zagreb said it was "deeply shocked."
Police have filed criminal charges against 23 people "suspected of ... publicly inciting violence and hatred", a statement said.
Six people are in custody, police are processing two more, and a search is under way for the remaining 15, the statement added.
If tried and convicted, the suspects face up to five years in prison.
Hajduk Split, who won the game 2-1, apologised to UEFA and Ajax, one of whose nicknames is 'the Jews', having "witnessed scenes which we do not want Europe to remember," while the Croatian football federation condemned the incident.
Ultra-nationalist hardcore fans have tainted Croatia's image for years, notably by chanting pro-fascist slogans and displaying Ustasha symbols.
The regime killed and persecuted hundreds of thousands of ethnic Serbs, Jews, Roma and anti-fascist Croatians.
Croatia were docked a point by UEFA after their fans painted a swastika on the pitch in Split in 2015, ahead of a Euro 2016 qualifier with Italy.
The perpetrators were never found.
In recent years, Croatia has seen a growing tolerance for its pro-Nazi past and critics accuse authorities of failing to sanction the use of Ustasha emblems.
