Jaymie Stuart Hall suffered a number of serious injuries during a disturbance in Dumbryden Gardens, Wester Hailes, at about 21:25 on Saturday.
The 35-year-old was taken to the Royal Infirmary of Edinburgh but died a short time later.
The arrested man is expected to appear at Edinburgh Sheriff Court on Tuesday.

Trustees of the Cwmaman Institute said they had six-figure debts and were struggling to keep the building open.
Opened in 1892 for the local mining community, the building had a Â£3.8m lottery-funded facelift in 2001 unveiled by the Prince of Wales.
Trust chairman John Oliver said they were warning groups using the venue it faced closure by the end of the year.
"It's been a struggle for a number of years, and we've been running it on a voluntary basis for the main part," he said.
"We hope something will crop up - we've written to Stereophonics but haven't heard back from them yet," Mr Oliver added.
"We'd be pleased if they said they could help us."
Stereophonics - formed in Cwmaman in the 1990s by Kelly Jones, Richard Jones and the late Stuart Cable - played some of their first gigs at the institute before winning international fame.
In July trustees sold a neighbouring pub - the Shepherd's Arms - to raise funds as part of the effort to save the venue.
A 41-year-old man has been charged with murder following the death of a man in an Edinburgh street.
[NEXT_CONCEPT]
Rock stars Stereophonics have been asked to help save a venue where they played some of their first gigs.