The game on Friday was played behind closed doors following crowd trouble – including racist chanting – in Croatia's 5-1 home win over Norway in March.
It was unclear whether the swastika was mowed into the grass or painted on the pitch, and attempts by ground staff to cover it up during the half-time interval were unsuccessful, according to Eurosport.
— Cezar (@CezarOtelul) June 12, 2015
Croatian football association (HNS) press officer Tomislav Pacak told the Balkan country's media, "We apologise to all fans watching the game on television, to both teams and to our guests from Italy for the Nazi symbol."
"As far as we have learned, the symbol was imprinted into the pitch between 24 and 48 hours before the match so that it could be visible during the game.
"This is sabotage and a felony, hence we expect police to identify the perpetrators and we have also notified UEFA.
"This is a disgrace not just for the HNS but for the whole of Croatia. Neither our coach nor players will comment."
UEFA has sanctioned Croatia before for repeated racist offences and crowd trouble by its supporters.
A number of Croatian fans formed a human swastika in the stands during a friendly with Italy in Livorno in 2006 and they also gave Nazi salutes.
Want to see Croatia fans stood like a Swastika in Livorno? Of course you do pic.twitter.com/f5T9aZAlP4
— Charles Ducksbury (@cducksbury) January 23, 2014
Davor Suker, Croatian FA president and former Arsenal striker, said: "It's one of our problems and we are working to fix it. Unfortunately something happened tonight too, but we would prefer not to talk about it now, we'll talk about it from tomorrow."
The game against Italy finished 1-1 Striker Mario Mandzukic gave Croatia a controversial 11th-minute lead before Antonio Candreva equalised with a cheeky penalty in the 36th.
The result leaves Croatia on top of Group H, two points above Italy with three games left to play.
Croatia faces one more game at home against Bulgaria at on the 10 October, which could be played behind closed doors again if UEFA punish them for the symbol.