Rasheeda Bibi, 53, from Sialkot district's Diawara village, was killed as she crossed the border on Thursday night after losing her way, Dawn reported.
Bibi was killed in the Pargwal sector of Akhnoor tehsil.
Citing police sources, the paper said that the woman was mentally ill.
Indian border authorities later handed over the body to her family in the presence of officials of Pakistan Rangers.
"A protest erupted in Bibi's native village after it emerged that she had been shot dead by BSF personnel," the paper said.
In August, a 17-year-old Pakistani boy was shot dead after entering Indian territory by mistake, the paper said.
Ijaz, from Kasur sector, was grazing cattle near the border when the incident had taken place.