The 39-year-old Renzi, whose country currently holds the European Union's rotating presidency, was expected in Maputo on Saturday, Brazzaville on Sunday and Luanda on Monday.
Italian media said Renzi was aiming to put a new focus for EU foreign policy on Africa and the Mediterranean region, particularly on the issue of immigration.
"It is hardly a coincidence that his first foreign trip during the EU presidency is to Africa," L'Unita daily said.
Hundreds of migrants - mainly from Eritrea and Syria but also from sub-Saharan Africa - are landing on Italian shores every day as they flee wars and poverty.
The government did not release further details about the trip but Italy has major economic ties to Africa and its energy major ENI is the largest foreign oil producer on the continent.
Renzi's first trip after being appointed prime minister this year was to Tunisia.