The incident occurred in the remote town of Thul in the interior Sindh province which remained shut down in most parts on the call of the Mutthaida-e-Qaumi Movement (MQM).
Police said the woman died after she was hit in the head by a stray bullet fired by around 100 activists of the Pakistan Muslim League (N) to celebrate the appointment of Sharif as Prime Minister.
"Musammat Bibi, 45, died on the spot while her 19-year old niece Jamila Bibi also sustained gunshot wounds and is in critical condition," one official said.
The MQM, which is the single largest party in Pakistan's biggest city Karachi, had called for the peaceful strike after three of its workers were executed yesterday.
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Karachi and some other parts of the province wore a deserted look as markets, business, petrol pumps and schools remained closed while public transport was also scare on the roads.
Public transport was off the roads in all major cities of Sindh, while petrol pumps and CNG stations were shut down.
The MQM central coordination committee while thanking the people for supporting the strike also called on the Chief Justice and government to take notice of the killings and disappearance of its workers and supporters.
He made it clear that if the government didn't act, the people would be forced to take the security into their own hands.