The body of Katy Rourke, who was from Broughty Ferry, Dundee, was found at the flat in Minto Street, in Craigton, at about 17:05 on Wednesday.
Police Scotland said a 26-year-old man had been arrested and was detained in police custody.
He was expected to appear at Glasgow Sheriff Court on 2 January. A report will be sent to prosecutors.
Officers have been conducting door-to-door inquiries and reviewing CCTV footage.
A man has been arrested in connection with the death of a 25-year-old woman at a flat in Glasgow.