Thousands of protesters began a hunger strike in Gauhati, the capital of India's northeastern state of Assam, the morning after rioters defied an overnight curfew and police fatally shot two demonstrators.
Abe was scheduled to travel to Assam and Manipur states on Sunday for a three-day trip to discuss security and economic ties with Indian Prime Minister Narendra Modi.
"Both sides have decided to defer the visit," Indian External Affairs Ministry spokesman Raveesh Kumar said in a statement.
Japan's Chief Cabinet Secretary Yoshihide Suga had earlier told reporters in Tokyo that security was being assessed.
Violence in Assam has been raging since late Wednesday, when India's upper house of Parliament passed the citizenship bill.
Indian police had to escort an advance team of Japanese security officials to their hotel on Thursday as protesters uprooted telephone poles, set buses and other vehicles on fire and attacked homes of officials from Modi's governing Hindu nationalist Bharatiya Janata Party.
Authorities relaxed the curfew for six hours on Friday in parts of Assam but shut schools until next week.
The protesters in Assam oppose the legislation out of concern that migrants will move to the border region and dilute the culture and political sway of those who already live there.
The new citizenship act, which the ceremonial president signed into law late Thursday, will grant Indian nationality to Buddhists, Christians, Hindus, Jains, Parsis and Sikhs who fled Pakistan, Afghanistan and Bangladesh because of religious persecution before 2015. It does not, however, extend to Rohingya Muslim refugees who fled persecution in Myanmar.
Critics have said the law violates India's secular constitution.
Challenges have already been filed with the Supreme Court.
Home Minister Amit Shah rejected criticism the legislation was anti-Muslim, saying it did not affect the existing path to citizenship available to all communities.
Bangladesh's foreign minister postponed a scheduled trip to India on Thursday for reasons Kumar said were unrelated to the citizenship bill.