Police were called to Princess Way at around 03:00 GMT on Sunday. A man, 34, was taken to Morriston Hospital but later died.
No weapons were used during the incident, but his death is being treated as suspicious.
The 23-year-old arrested man is in custody at Swansea police station.
The area remains cordoned off while police examine the scene.
The man's family have been informed and are being supported by specially-trained officers.
A man has been arrested on suspicion of murder following the death of a second man after an incident in Swansea city centre.