The public prosecutor of Ravenna, in Emilia-Romagna, opened a case on Thursday to find the culprit, ANSA news agency reported.
Kyenge, the minister for integration, was speaking at a Democratic Party (PD) rally last Friday when the incident happened.
She responded via Twitter, saying "it was a waste of food in tough economic times".
The incident came less than two weeks after Northern League MP Roberto Calderoli called Kyenge an "orangutan", sparking outrage and calls for his resignation.
Calderoli kept his post as vice president of the Senate, but a defamation case has been launched against him.
Kyenge, who is trying to overhaul Italy's immigration system, has previously said that she receives daily threats and has bodyguards.