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 now be held until 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”.