The IUML will argue that the proposed law violates the constitution.
The Citizenship (Amendment) Bill (CAB), which is set to become law after it was cleared by both houses of parliament amid opposition protests, will now face the Supreme Court test.
The Indian Union Muslim League (IUML) has approached the Supreme Court against the citizenship bill. Its petition argues that the proposed law violates the constitution by allowing citizenship based on religion.
The bill provides for Indian citizenship to non-Muslims who fled Pakistan, Bangladesh and Afghanistan and entered India before 2015.
The opposition in parliament argued that the bill violates Article 14 of the constitution, which promises the right to equality and equality before law.
Congress leader and former union minister P Chidambaram, who spoke in the Rajya Sabha last evening before the vote on the bill, said the CAB is unconstitutional and "the battleground shifts to the Supreme Court".
Many Congress leaders have indicated that the party may challenge the bill in court.
"It is certainly legislation highly suspect in constitutionality in terms of basic structure and legal validity.
"I have no doubt that it deserves to be challenged and will in the near future be challenged (in court)," Abhishek Manu Singhvi, a Congress spokesperson and a senior lawyer, told Press Trust of India.
Asked if the Congress would approach the Supreme Court against the Bill, Congress general secretary KC Venugopal said, "We will explore all possibilities."
A former Chief Justice of India, RM Lodha, said "exclusion or inclusion on the basis of religion may not meet the touchstone of the constitution".
Home Minister Amit Shah, while defending the bill in parliament, said it made a "reasonable classification" and so is legally sound.
Constitutional expert Subhash Kashyap says it is an argument that could stand in court. "The Constitutional position is that Article 14 guarantees equality before the law. Several judgements of the Supreme Court have said that reasonable classification is permissible and if the classification is reasonable, then there is no violation of the fundamental right. The question will be whether the classification between infiltrators and refugees is reasonable. If that classification is reasonable, then there will be no violation of Article 14," Mr Kashyap told news agency ANI.