STORY: The son of the dead woman, Oleksandr Novikov, survived the attack despite bricks from a wall falling on to him as he slept.
Novikov said emergency services tried to retrieve his mother from underneath the rubble for an hour and a half.
"I knew exactly where she was, so I told them where to dig. When they dug her out, her limbs were already blackening," he said, adding that he thought this meant the explosion immediately killed his mother.
Clothes and boots could be seen strewn around the site of the strike, and men wearing war crimes prosecutors' protective vests inspected the area.
Regional governor Oleh Synehubov wrote in a post on the Telegram messaging service on Tuesday that a woman was killed on the outskirts of Kharkiv after a strike.
Kharkiv, Ukraine's second-largest city, is close to the Russian border and has been under constant shelling throughout the conflict.