The slain jawan was identified as 28-year-old constable Sitaram Upadhyay. He hailed from Giridih in Jharkhand and joined the force in 2011.
Upadhyay is survived by a three-year-old son and a one-year-old daughter, they said.
"Firing in Heeranagar area was on during the intervening night of May 16 and 17 in which one BSF trooper was injured. Yesterday, during the daytime, it stopped but Pakistan resumed firing last night in Arnia sector which claimed the life of a jawan early today," a senior official of the border guarding force said.
The official added that in R S Pura sector of the IB in Jammu, unprovoked shelling of mortars and heavy fire from the Pakistani side started at about 4 am today which was being "suitably countered" by the BSF units.
"The firing in R S Pura sector is intermittent," he said.
The incidents of unprovoked firing and attempts to infiltrate the IB have increased in the last few days even as Prime Minister Narendra Modi is expected to reach Jammu and Kashmir tomorrow as part of an official visit.
A BSF jawan was killed along the Jammu border area earlier this week while he was thwarting an infiltration bid.