A group of plaintiffs brought the case to protest against the government's Aadhaar programme, which has recorded the fingerprints and iris scans of more than one billion Indians.
They argue that although the right to privacy is not explicitly set out in India's constitution, it nevertheless guarantees it implicitly.
"Our constitution gives us liberty to live life," Gopal Subramanium, a lawyer for the plaintiffs, argued before the court.
"Liberty existed even before the constitution was drafted and it includes privacy," he added.
"There cannot be a question of diminution but expansion of a right. Right to liberty includes freedom from encroachment on his or her privacy."
Prime Minister Narendra Modi's government has rejected suggestions that the programme, set up in 2009, poses a threat to civil liberties.
The Aadhaar database was originally presented as a purely voluntary programme that offered to provide every Indian with an identity card.
In recent years however, it has become compulsory for a growing number of services, such as the opening of bank accounts, the payment of taxes and any payment of public money.
Its critics say that its use for what are effectively essential services means that Indians' right to privacy is being increasingly violated.
"If you have the same number in every single database, travel, phone, banking, then anyone sitting in the Home Ministry or intelligence bureaux will be able to pull out information on me," argued Reetika Khera, an economics professor at Delhi's Indian Institute of Technology.
"It will be a landmark case and it will be law for many many years to come. I think it is significative because privacy (is) at the root of every good democracy," she added.
The government will present its arguments on Thursday and the court's ruling could be handed down in the coming months.
Eyewitness? Submit your stories now via social or:
Email: news@pulselive.co.ke
