Melek Alpaydin, 38, was eating breakfast when the shell hit her apartment in the Sur district of Diyarbakir, the Dogan news agency said.
Photographer at the scene said the mortar fire had left a gaping hole in the exterior wall of the second-story apartment.
Bloodstained breakfast trays, tea glasses and bowls could be seen lying on the carpet where she was sitting which was also covered in debris from the damaged wall, as local women wailed in mourning outside, he said.
Dogan said it was not clear where the shell had been fired from but that an investigation was under way.
Much of the city’s Sur district has been under a blanket curfew since early December as Turkey security forces seek to drive out militants from the Kurdistan Workers Party (PKK).
The curfew is one of several highly-controversial measures imposed on towns in the southeast where the armed forces are waging a relentless campaign against the rebels.
The government says such measures are needed to flush out PKK fighters who have effectively taken over towns by erecting barricades and digging trenches.
But Kurdish activists say the use of force has been wildly excessive with the opposition Peoples’ Democratic Party (HDP) saying 12 civilians have been killed in Sur alone since the curfew was imposed on December 2.
The army says 55 “terrorists” have been killed in Sur since the operation began. With the curfew-affected area closed to the media, it has not been possible to independently verify the figures.