Images from the city’s Seelampur area showed stone-throwing crowds confronting police officers. Police retaliated with tear gas and batons.
Local reports say several protesters and officers were injured.
The protest comes days after clashes between police and protesters in Delhi left at least 50 people injured.
The new law offers citizenship to non-Muslims from three nearby countries.
Seelampur, in the east of the city, has a large Muslim population. Protesters are claiming that the act will marginalise them.
There were reports of a police station being set on fire, and police said buses were vandalised.
Meanwhile on Tuesday, the Supreme Court refused to hear a petition against the police action inside Delhi’s Jamia Millia Islamia University, where they allegedly attacked students inside campus premises, including the library and toilets.
Chief Justice Sharad Bobde said the top court did not have to intervene since it was “a law-and-order problem”. He also told lawyers to file petitions in trial courts.
More protests broke out, including at Jamia Millia Islamia.
Prime Minister Narendra Modi said the new law did not affect any citizen of India of any religion but was “for those who have faced years of persecution outside and have no place to go except India”.
But some say the Citizenship Amendment Act (CAA) is discriminatory and part of a “Hindu nationalist” agenda to marginalise India’s 200-million Muslim minority.
Others – particularly in border states – fear being “overrun” by new arrivals from Afghanistan, Bangladesh and Pakistan.
What is the law about?
The Act offers amnesty to non-Muslim illegal immigrants from three neighbouring Muslim-majority countries.
It amends India’s 64-year-old citizenship law, which currently prohibits illegal migrants from becoming Indian citizens.
It also expedites the path to Indian citizenship for members of six religious minority communities – Hindu, Sikh, Buddhist, Jain, Parsi and Christian – if they can prove that they are from Pakistan, Afghanistan or Bangladesh. They will now only have to live or work in India for six years – instead of 11 years – before becoming eligible to apply for citizenship.
It also says people holding Overseas Citizen of India (OCI) cards – an immigration status permitting a foreign citizen of Indian origin to live and work in India indefinitely – can lose their status if they violate local laws for both major and minor offences and violations.
Opponents say the law is exclusionary, is part of an agenda to marginalise Muslims, and violates the secular principles enshrined in the constitution. They say faith cannot be made a condition of citizenship.
However, the government led by the Hindu nationalist Bharatiya Janata Party (BJP), says it is only trying to give sanctuary to people fleeing religious persecution.
What happened in Delhi?
This was the third straight day of protests in the capital, after a student protest on Sunday turned violent and left dozens injured.
Many of the injured were participating in protests at universities in Delhi.
Ten people, many of whom have “criminal backgrounds”, have been arrested, Delhi police said on Tuesday. Amid criticism for using “excessive force” inside campus premises, they added that no students were detained.
Police said locals who lived near the campus had joined the protests and attacked officers.
A hospital spokesperson said two people were admitted with bullet wounds, according to local media – something denied by police.
The BBC has seen the medical report of a third person – who said he was a passer-by, not a protester – who thought he had been shot in his thigh.