Durham police were dispatched to the building on Wayne Avenue, near Taunton Road and Simcoe Road, at 12:23 a.m. where the elderly woman was found suffering from obvious trauma.
She has been identified by police as Alletta Rusnell.
Police said 34-year-old Sharon Baksh was arrested without incident at the apartment and has been charged with second-degree murder.
Police have not said what may have led to the dispute between the two women.
Baksh is being held in police custody and her next court appearance is scheduled for June 24, 2013.Police said Rusnell's death is the first homicide in Durham Region in 2013.