The woman, named as Karen Gallagher, was found dead within a flat in Burnfield Road, Thornliebank, on Wednesday.
A report will be submitted to the Procurator Fiscal and the suspect is expected to appear at Glasgow Sheriff Court today.
Man arrested over death of woman
A 47-year-old man has been arrested and was in police custody last night in connection with the death of a 31-year-old woman found dead in Glasgow.