The draft resolution had been brought by six groups representing 626 of 751 members of the European Parliament.
The vote, which was expected to conclude on Thursday, will now not be held until the end of March.
The resolution had described the CAA as “fundamentally discriminatory in nature”, with one group saying the controversial bill had the potential to “create the largest statelessness crisis in the world”.
It also criticised a recent crackdown in Kashmir, including an internet shutdown and preventive detention measures.
The vote will be held after Prime Minister Narendra Modi‘s March 13 visit to Brussels for a bilateral summit.
Local media reported that New Delhi was calling the postponement a “diplomatic victory”.
However, the development will suit both sides, observers said.
“I think the Europeans are giving Prime Minister Modi the benefit of the doubt because he will be coming to Brussels for a summit next month,” Jyoti Malhotra, editor of national and strategic affairs at The Print website in New Delhi, told Al Jazeera.
“It would have looked very bad for him had the European Parliament passed a resolution which was critical of the CAA and Kashmir. So I think both India and Europe are saving face.
“The Europeans don’t want to antagonise a big democracy like India. President Trump will be visiting here at the end of February so the Europeans wouldn’t want to be completely left out of the story,” she added.
Members of the European Parliament who had called for the delay said it would give them more time to study the details.
Gareth Price, senior research fellow at London-based international affairs think-tank Chatham House, said uncertainty around the bill would have contributed to the delay.
“How the CAA is rolled out, whether it’s rolled out, whether the Supreme Court amends it, we aren’t actually at that point yet,” he told Al Jazeera.
“In terms of human rights, it doesn’t look great, but it’s difficult to criticise something when we don’t really know what will look like. The situation in Kashmir is more clear cut but the two issues have been rolled into one, and one of them hasn’t happened yet.”
Three months ago, a delegation of nearly 30 members of the European Parliament from far-right parties was invited for an unofficial visit to Kashmir – the first group of people allowed access to the region after India revoked its special status, known as Article 370.
London-based Kashmiri lawyer Mirza Saaib Beg said the Indian government’s lobbying efforts with members of the European Parliament may also be a factor.
“It was interesting to note that the decision to defer was floated by the European People’s Party, which is a centre-right party. So one could wonder how much of an influence Modi’s outreach to right-wing political groups outside of India has played a role in this.”
The CAA bill seeks to fast-track citizenship to Hindus, Sikhs, Buddhists, Jains, Parsis and Christians who fled religious persecution in neighbouring Afghanistan, Bangladesh and Pakistan, but excludes Muslims.
Anti-CAA protesters, who have taken to the streets across India in recent weeks, call the bill a violation of the Indian constitution – a claim the ruling Bharatiya Janata Party (BJP) denies.
“It is pivotal, indispensable right now for the Europeans to speak out about this,” Beg said.
“Indian media have not been able to criticise the government and there’s been an absolute dereliction of duty on the part of the Supreme Court.
“What is now unfolding is an authoritarian regime that is imposing its own puritanical definition of citizenship.
“And in the context of Kashmir, we are now six months without any communication. So it is a crisis on which the European Parliament definitely needs to take an urgent stand.”