Emmanuel Chidi Nnamdi, 36, escaped to Italy last in November 2015 with his wife Chinyery after the Islamist militants murdered their families at a church earlier that year.
On the way their baby died and the couple was taken in by a Christian charity.
Police have arrested 35-year-old Amedeo Mancini on suspicion of racially-aggravated manslaughter.
Italian Prime Minister Matteo Renzi condemned the incident on Twitter:
Il Governo oggi a Fermo con don Vinicio e le Istituzioni locali in memoria di #Emmanuel
— Matteo Renzi (@matteorenzi) 7 July 2016
Contro l'odio, il razzismo e la violenza.
He said: "The Government today in Fermo with Don Vinicio and local institutions remember #Emmanuel. Against hatred, racism and violence."
Geoffrey Onyeama, Nigeria's Foreign Minister, also responded to the incident:
Italy must do justice on the racist killing of Nigerian: #Emmanuel in Fermo. @AngeAlfa @PaoloGentiloni @MatteoRenzi pic.twitter.com/JFRPADNo20
— Geoffrey Onyeama (@GeoffreyOnyeama) 8 July 2016
Authorities say a fight broke out between the pair in the eastern town of Fermo which led to Emmanuel Nnamdi being hit with a traffic pole.
He was sent to hospital in a coma but never recovered.
Amedeo Mancini's lawyer says he never meant to kill Mr Nnamdi and that he punched him in self-defence.
Fr Vinicio Albanesi, who married Emmanuel and Chinyery in Italy, has said that churches helping migrants have had projectiles thrown at them.
