On Sunday, Luigi di Maio called on the European Union to impose sanctions on France for its policies in Africa.
He said France had "never stopped colonising tens of African states".
Italy and France have previously clashed on issues linked to migration. Italy is the destination for thousands seeking a new life in Europe.
Last year, France criticised Italy for not allowing rescue boats carrying migrants in the Mediterranean to dock. Italian officials responded by accusing France itself of refusing to accept migrants.
Mr Di Maio, leader of the Five Star Movement (M5S) which governs in coalition with the far-right League party, made his latest comments during a visit to central Italy at the weekend.
It came as the UN said about 170 migrants were feared drowned in two separate Mediterranean shipwrecks.
"The EU should sanction France and all countries like France that impoverish Africa and make these people leave, because Africans should be in Africa, not at the bottom of the Mediterranean," he said.
"If people are leaving today it's because European countries, France above all, have never stopped colonising dozens of African countries."
He said if it wasn't for Africa, France would rank 15th among world economies, not in the top six.
The Italian ambassador to France, Teresa Castaldo, was summoned to the foreign ministry in Paris on Monday.
French diplomatic sources quoted by Italian news agency Ansa called Mr Di Maio's remarks "hostile and without cause given the partnership between France and Italy in the European Union".
But Mr Di Maio, who is also labour and economy minister, was unrepentant on Monday.
He accused France of manipulating the economies of African countries that use the CFA franc, a colonial-era currency backed by the French treasury.
"France is one of those countries that by printing money for 14 African states prevents their economic development and contributes to the fact that the refugees leave and then die in the sea or arrive on our coasts," he said.
"If Europe wants to be brave, it must have the courage to confront the issue of decolonisation in Africa."
France says the CFA franc is a guarantee of financial stability but others have attacked it as a colonial relic.
The International Organisation for Migration (IOM) says 4,216 migrants have crossed to Europe by sea in the first 16 days of 2019 - more than double the number arriving in the same period last year.
Italy's other Deputy PM, Matteo Salvini, wrote on Facebook after the latest deaths in the Mediterranean that "as long as European ports remain open... unfortunately the smugglers will continue to do business and kill".