In the two-page order, Justice Abraham also dismissed Pakistan's contention that the court had no jurisdiction over the case. In April, a military court sentenced him to death for alleged involvement in spying and subversive activities.
She said Pakistan will vigorously fight this case without compromising on its national security.
While presenting arguments, Pakistani counsel had informed ICJ that Jadhav, 46, was arrested in March a year ago in the restive Balochistan province.
The case - a rare foray for the two South Asian nations into the worldwide courts - has highlighted the recent sharp upsurge in tensions between the nuclear-armed rivals.
It also told Pakistan to give consular access to India.
He said Pakistan has already informed the ICJ that it does not accept its jurisdiction in matters related to the national security. The next day, the global court gave Jadhav a lease of life and stayed the death sentence as a provisional measure.
The Hague-based court had yesterday stayed the execution of Jadhav, 46, considered to be a spy by Pakistan. India was able to demonstrate Pakistan's disregard for global conventions and its propensity to undermine the rule of law.
Sushma Swaraj said that ICJ order has come as great relief to family of Jadhav and thanked Harish Salve for presenting India's case effectively.
A new team of lawyers would present Islamabad's position more effectively in the world court at The Hague, Pakistan's Foreign Affairs Advisor Sartaj Aziz was quoted by media reports as saying today; he also commented that the counsel for Pakistan had "courageously" presented their stance earlier this week.
In 1998, a Paraguayan man was executed for murder in Virginia despite the global court's order urging the United States to halt his execution in a similar case involving the right to consular access. Now it is over to round two where both India and Pakistan would put out arguments before the ICJ which would pronounce its final verdict probably by August.
In November previous year, Pakistan withdrew six officials from its mission in Delhi after they were outed as suspected spies by India.
He said Jadhav "has confessed to having been sent by India to wage terror on the innocent civilians and infrastructure of Pakistan".
Pakistan was in shock as it was confident that the ICJ will throw out the case on the grounds of jurisdiction. As such, India has the rights of consular access as outlined in the article concerned.
"Pakistan should have provided Kulbhushan with the consular access from the start", said lawyer Yasser Latif Hamdani to DunyaNews.