Prime Minister Narendra Modi's government says the new law will save religious minorities such as Hindus and Christians from persecution in neighboring Bangladesh, Pakistan and Afghanistan by offering them a path to Indian citizenship.
But critics say the law, which does not make the same provision for Muslims, weakens India's secular foundations.
On Sunday protesters in South Delhi, including locals and students from Jamia Milia University, torched some buses, cars and two wheelers.
A Reuters witness said police resorted to baton charges and firing tear gas on the protesters to disperse them.
Some injured protesters were taken to a nearby hospital, according to the Reuters witness, but police have not given injury toll figures.
Demonstrators also held peaceful protests in Guwahati and Dehradun.