Relations between the two countries have plummeted in recent months, with India blaming Pakistan for a raid on an army base in its part of disputed Kashmir in September that killed 19 soldiers.
Delhi responded with what it called "surgical strikes", infuriating Islamabad.
"Due to Indian unprovoked firing last night a civilian, Muhammad Latif of village Janglora, and a minor Haniya, age one and a half, embraced shahadat (martyrdom) while seven civilians were injured," a Pakistani military statement said.
The firing took place across the border between Indian-held Kashmir and Pakistan's Punjab province in the villages of Harpal, Pukhlian and Charwah, the statement said, AFP reported.
Sunday night's incident comes days after Indian border security forces said they shot dead seven Pakistani soldiers in retaliation for a ceasefire violation, with Pakistan refuting the claims.
Kashmir has been divided between India and Pakistan, but claimed in full by both, since the two countries gained independence from Britain in 1947.
Since 1989 several rebel groups have been fighting Indian forces deployed in the region, seeking independence or a merger of the territory with Pakistan.