The guard was captured on April 23, the day after an attack on the Indian-controlled part of Kashmir.
Nearly 30 people are reported to have been killed in the attack. No group has yet taken responsibility for the attack, but India has accused Pakistan of having supported it.
The handover of the border guard "was carried out peacefully and in accordance with established protocols", says India's border troops in a statement.
On Wednesday, Pakistan's army reported that 40 civilians had been killed in the clashes between the countries, of which half were women and children, and a further 13 soldiers had been killed.
India, in turn, has announced that 15 civilians and five soldiers had been killed on their side.
