"This is sabotage and a felony," said Tomislav Pacak, a Croatian Football Federation (HNS) spokesman. "We expect police to identify the perpetrators.
"This is a disgrace not just for the HNS but for the whole of Croatia."
The game was played behind closed doors after Croatia were punished for racist chants by fans against Norway in March.
Pacak added that Uefa had been told about the incident, which overshadowed the 1-1 draw between the two sides who are vying for top spot in Group H.
The swastika - widely recognised as the symbol of Nazi Germany - was seen during the first half and although ground staff at the stadium in Split tried to cover it up at half-time they were not successful.
It is unknown whether the symbol was mowed or painted into the grass, or who is responsible.
"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," added Pacak.
"We apologise to all fans watching the game on television, to both teams and to our guests from Italy for the Nazi symbol."
November's reverse fixture in Milan was stopped twice for crowd trouble, with riot police involved.
Croatia were forced to close part of their stadium for March's game against Norway as a punishment for their fans' behaviour at the San Siro.
But the supporters who did attend the Norway game caused more problems, leading to the Italy game to be played in an empty stadium.
"It's one of our problems and we are working to fix it,'' said Davor Suker, the president of the Croatian football association. "We'll speak about it on Saturday, but I'm very angry."
The Croatian Football Federation has apologised after a swastika symbol was marked on to the pitch ahead of their Euro 2016 home qualifier against Italy.