Agnius Naumovas, who was from Lithuania but had been living in the city, was found on Margaret's Avenue at about 20:00 local time on Christmas Day.
He was taken to hospital, where his injuries were described as serious.
Mr Naumovas, who was 29, died on Thursday evening.
A post-mortem examination has been carried out by the Irish state pathologist.
A 41-year-old man was arrested in Waterford on Friday morning.
A man in his 40s has been arrested after a man found with head injuries in Waterford city centre on Christmas Day died in hospital.