An army statement said that a captain died and a soldier was seriously injured in the clash near Skardu.
It said the exchange of fire happened late on Tuesday night and continued on Wednesday morning.
Earlier this month, India accused Pakistan of killing five of its soldiers near the LoC.
The Skardu clash is the latest in a series of accusations and counter-accusations, with each side blaming the other for violations of a 2003 ceasefire.
Thousands of people have been killed in Indian-administered Kashmir since an armed revolt against Indian rule erupted in 1989.
A Pakistani military statement said that the captain had been killed by “unprovoked shelling” by India.
The Indian army and government have yet to comment officially on the Pakistan claims, but an army source told the BBC in Srinagar that it was Pakistan who was guilty of the latest ceasefire violation.
“We retaliated,” the source said, “and there have been no casualties on our side.”
Indian Defence Minister AK Antony said on Monday the army would take “all possible steps” to counter ceasefire violations by Pakistan along the LoC.
Last week Indian Prime Minister Manmohan Singh said that ties with Pakistan cannot improve until it “stops using its territory for anti-India activity”.
In a speech marking Independence Day he described the killing of five Indian soldiers on 6 August, allegedly by Pakistani troops, as a dastardly act.
Pakistan strongly denied any responsibility for the killing of the Indian troops. It says that a few days before they died, Indian troops crossed the LoC to abduct and kill four civilians in the Neelum valley area.
However Prime Minister Nawaz Sharif has said that despite the violence, it is imperative to restore the ceasefire on the LoC.
Claimed by both countries, Kashmir has been a flashpoint for more than 60 years.
Violence has fallen in recent years, although a series of clashes along the LoC since January has left a number of soldiers and civilians dead on either side and strained relations.
Correspondents say the bad-tempered mutual accusations have called into question the possibility of the two prime ministers meeting on the sidelines of the UN General Assembly next month.