Residents with any information have been urged to contact the concerned authority
"This bill is in line with India's centuries old ethos of assimilation and belief in humanitarian values," Prime Minister Narendra Modi tweeted, adding that he was "delighted" about its passage.
Modi's government had tried to shepherd the legislation through parliament during its first term in power, but it failed in the upper house, where Modi's Bharatiya Janata Party (BJP) and its allies lack a majority.
After sweeping to victory in the April-May national elections, the BJP is now more confident it can push the bill through both chambers.
During a lengthy debate marked by angry exchanges, opposition Congress lawmaker Shashi Tharoor said the bill "infringes upon the principle of equality before law" guaranteed to all persons, including non-citizens.
The legislation seeks to amend the Citizenship Act of 1955, which prohibits illegal migrants from applying for Indian citizenship.
On Monday, 100 scientists and scholars at institutions in India and abroad published a joint letter expressing their "dismay" at the legislation, saying the constitution called for members of all faiths to be treated equally.
But, they wrote, Modi's "proposed bill would mark a radical break with this history and would be inconsistent with the basic structure of the constitution".
The letter said such a careful exclusion of Muslims would "greatly strain" India's pluralism.
"What are we doing now? We are giving the minority their rights."
Shah has recently also proposed a "national register of citizens" that would see "each and every infiltrator identified and expelled" from India by 2024.
The citizenship bill has led to protests in India's northeastern states, where residents are unhappy about an influx of Hindus from neighbouring Bangladesh.
In Guwahati in Assam state, protestors set fire to tyres, while tribal groups staged protests in Tripura.
On Monday, prominent political groups opposing the bill called for a complete shutdown across all the states in the northeast on Tuesday.
Residents with any information have been urged to contact the concerned authority
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