Officers said the 24-year-old had been detained in police custody in connection with a serious sexual assault in Queen's Park on 30 March.
The park, at Pollockshaws Road and Balvicar Street, was cordoned off while police investigated the incident.
A report will be submitted to the procurator fiscal, Police Scotland said.
Police investigating the rape of a 37-year-old woman in a popular Glasgow park have arrested a man.