Croatian police are investigating the alleged burning of a swastika into the grass of the stadium which hosted the Euro 2016 qualifier between Croatia and Italy.
They took samples of soil from the pitch after the game and questioned employees of the company maintaining the grass.
The match - which ended in a 1-all draw - was played behind closed doors, after UEFA found Croatian fans guilty of racist chanting during a qualifier against Norway in March.
Croatian football federation chief Davor Suker has apologised for the incident and urged the authorities to punish the perpetrators.
"I am saddened and upset with what has happened last night. I again urge all institutions of the Croatian state to carry out a thorough investigation and punish those responsible," Suker said.
The nation's president, Kolinda Grabar-Kitarovic, reacted as well.
"Croatia has ... a very serious problem with hooligans who aim to discredit not only Croatian football, but the Croatian state," she said in a statement, adding that she "demands a vigorous investigation" of the incident.
The swastika - the symbol of Nazi Germany - was visible only under the floodlights and from higher tiers in the stands, and it appears to have been be etched into the field with chemicals.
Croatia has an ugly history in this area.
FIFA banned Croatian veteran Josip Simunic from the 2014 World Cup after he urged the crowd to chant a Nazi salute, similar to those that led to fines after previous games.
Croatia has paid more than 500,000 euros ($A725,794.75) in fines over the past 10 years for frequent violations for similar incidents and is on UEFA's special monitoring list.
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