"It's not the immigrants that are stealing places in kindergarten; they pay taxes.
"It's tax evaders that steal places in kindergarten. It's the people who exploit other people's work, not foreigners," Kyenge said during a speech at the British ambassador's residence in Rome.
"Our enemies are not those who try to contribute but those who don't stick to the rules - this has no colour," the minister added.
Congo-born Kyenge, who since becoming minister in April and has been the victim of several racist attacks, said Italians need to see the value that immigrants can bring to their country.
"Those who come are not coming to disrupt the country and rob jobs. They are bringing their traditions, their knowledge and interacting with the community," she said.
The minister was speaking just days after European leaders met in Brussels to discuss immigration and asylum policy, in the aftermath of the death of more than 300 migrants off the coast of Italy at the start of October.
More than 30,000 immigrants have arrived in Italy since the start of 2013, according to government estimates. While the coast guard regularly saves migrants from rickety boats en route to Italy, Kyenge said Italy must shift from an emergency approach to an integration policy.
"For a long time Italy has been reacting to emergencies and making it a problem of security," she said.
"There is a will to change our approach to integration, to stop this being considered an emergency and to build up a true policy of integration."
As the Italian government struggles to balance its books, Kyenge said revamping a 20-year-old immigration policy will also have financial benefits.
"We've seen lots of police action that have a high cost. I think integration policy costs less than a policy of oppression," she said.
The minister pointed to Cameroon, where nationals attend "schools for integration" before moving to Europe, as an example of a broader integration process.
"In Cameroon people are taught Italian and get to know the services. If we can do this we can review the concept of integration, which already begins before departure," Kyenge said.
She also renewed calls to overhaul Italy's citizenship law, which at present rules that a second-generation immigrant cannot become an Italian citizen until they are 18.
"Citizenship is a right. For children who are born here or who have come here very young, we need to bring them up with an equal opportunities approach.
"Ensure the future of those who might sit in government in the future," she said.