Two more soldiers and another civilian were injured in the latest violation by the Pakistan Army of the 2003 ceasefire agreement to maintain peace at borders and along the Line of Control (LoC), a police spokesman said.
The spokesman said the fresh cross-border firing incidents occurred in Rajouri and Poonch districts on the LoC that divides Jammu and Kashmir between the two countries.
The spokesman said the Pakistan Army used 82 mm mortar shells and automatic weapons to target Indian positions on the LoC and the soldier and the woman were killed in the Tarkundi sector of Rajouri.
The deceased woman was identfied as Rubina Kausar, 50. The identity of the slain soldier was not known immediately.
The Indian Army retaliated to the firing "effectively", said the spokesman.
(Pictures from RS Pura)
India and Pakistan have accused each other of regularly violating the ceasefire agreement between them to maintain peace at the border and the LoC.
Border skirmishes intensified after Pakistani militants attacked a military base in Jammu and Kashmir's Uri, killing 19 Indian soldiers on September 18.
The Uri attack prompted the Indian Army to carry out a surgical strike that destroyed seven terror launch pads and killed an unknown number of terrorists and their sympathisers in Pakistan-administered Kashmir, across the LoC.
Earlier on Monday, Pakistan Rangers indulged in shelling and firing on the International Border (IB) in R.S.Pura, Suchetgarh and Hira Nagar sectors of Jammu division.
"Pakistan Rangers fired mortars and used automatic weapons to target civilian and Border Security Force (BSF) facilities in R.S.Pura, Suchetgarh and Hira Nagar sectors," another police officer said.
The Pakistani shelling was retaliated by the BSF.
Heightened border tensions between the two countries have forced many residents of frontier villages to migrate to safer locations.
Residents of border villages close to the IB celebrated a subdued Diwali, away from home. Pakistan troops have been indiscriminately targeting their homes, cattle and crops.
Authorities have set up temporary accommodations -- in educational institutions, rural development department buildings and community halls -- for hundreds of border residents in Jammu, Samba and Kathua districts.
India shares 230 km of International Border and 740 km of LoC with Pakistan in Jammu and Kashmir. The boundary, manned by the paramilitary BSF runs through Jammu district and the LoC, which is not an internationally-accepted frontier, cuts across other regions of the state.