The game finished 1-1, to leave Croatia top of Group H by two points from Italy, but it could face further sanction by European governing body UEFA.
Croatia apology
Tomislav Pacak, a spokesman for the home federation, issued a statement about the incident on its official website Saturday.
"We apologize to all viewers, our guests from Italy and the players from both teams, for the Nazi symbol on the Poljud Stadium grass," he said.
"We have immediately notified UEFA of the incident.
"This was an obvious act of sabotage and a criminal act. We condemn it and ask the police and judicial bodies to find the person(s) responsible for what is a shame not only for Croatian football, but the entire country.
Read: Croatia star banned from World Cup for 'Nazi Chants'
"Once again, we express regret and condemn this act, and we apologize to all the viewers, guests and players from both teams."
Pacak claimed that a "chemical agent" had been used on the pitch, 24 to 48 hours before kickoff, timed to be visible during the qualifying match.
The stadium is the home of Croatian top-flight side Hajduk Split.