South Wales Police said it was called to Neath Road, in the Hafod area of the city, at about 13:35 BST on Tuesday.
The area has been cordoned off and an investigation is under way, police added.
A 35-year-old man has been arrested in connection with the death and is currently in custody at Swansea Central Police Station.
A man has been arrested following a sudden death in Swansea.