He is being held in connection with the death of Isabelle Sanders, 51, in the Crookston area of Glasgow at around 1.55am on Wednesday.
Ms Sanders's partner Norman Busby, 85, was also seriously injured in the attack in their house on Raeswood Drive.
Mr Busby remains in a high dependency unit at Glasgow's Southern General Hospital.
Police said the 19-year-old will appear at Glasgow Sheriff Court on Monday.
Mrs Sanders worked at the Lloyds branch on Waterloo Street in Glasgow, and her partner is a retired police officer.
A spokeswoman for Lloyds said: "Isabelle will be sorely missed."