Jason McCue, from East Kilbride, was seriously injured in John Hastie Park, Strathaven, on Tuesday. He was treated by paramedics but died at the scene.
Police Scotland previously said they were treating the 43-year-old's death as murder.
The 50-year-old who has been detained in police custody is expected to appear in court later.
Mr McCue was found in the park at about 13:30 on Tuesday following a disturbance.
A 50-year-old man has been arrested in connection with the death of a man in a South Lanarkshire park.