"Kyenge, Go Back to Congo" read a banner put up by the group in the central city of Macerata outside an office of the minister's leftist Democratic Party.
The group, Forza Nuova, said in a statement: "You cannot sell off Italian citizenship to elements that are foreign to our culture, just as we cannot force citizens to applaud a multi-racial society."
Kyenge and the Democratic Party have called for children born to immigrants in Italy to be given citizenship -- a proposal opposed by its coalition partner, the centre-right People of Freedom party.
Kyenge, 49, an eye doctor, arrived in Italy in 1983 from the Democratic Republic of Congo.
"They will not stop me. I want to start a debate and not impose any model," she said .
Kyenge has already been a target of insults from far-right groups, as well as lawmakers from the populist and xenophobic Northern League party.
Prime Minister Enrico Letta and his centre-right deputy Angelino Alfano were forced to defend her saying: "Cecile Kyenge is proud to be black and we are proud to have her in our government."