"The hearts of Muslims all over the world are grieving over the massacre of Muslims in India," Khamenei said in a tweet in English, just days after New Delhi rebuked Iran's foreign minister for commenting on the same issue.
"Iran condemns the wave of organized violence against Indian Muslims," Foreign Minister Mohammad Javad Zarif tweeted on Monday, in response to which New Delhi summoned the Islamic Republic's ambassador and lodged a protest.
"We do not expect such comments from a country like Iran," ministry spokesman Raveesh Kumar said in a statement later.
The citizenship law provides non-Muslims from Afghanistan, Bangladesh and Pakistan a fast track to Indian citizenship.
Prime Minister Narendra Modi's Hindu nationalist government says this is required to help minorities from those mainly Muslim countries.
Critics argue the law discriminates against Muslims and violates the spirit of India's secular constitution.
Hundreds of thousands of people have taken part in protests since December.
Earlier this week, the office of the U.N. High Commissioner for Human Rights said it intended to approach India's Supreme Court about the citizenship law.