Police confirmed a 26-year-old man had been arrested and was being held in connecting with the incident.
He is due to appear at Glasgow Sheriff Court today.
The 51-year-old woman was attacked early on Sunday morning.
It is understood that the woman was on her way to work when she was attacked in the park at about 5.45am on Sunday.
She did not require any hospital treatment.
Police Scotland forensic officers carried out extensive searches at Glasgow Green yesterday.