Jakob Lindenthal, a 24-year-old pursuing a master's degree in physics, said he took part in two rallies in the southern city of Chennai against the law, which critics say discriminates against India's minority Muslims.
A photo circulated on Twitter shows Lindenthal holding a sign that reads: "1933-1945 We have been there," a reference to Nazi Germany.
Lindenthal said he was summoned to a meeting with India's immigration authorities on Monday and told that he had violated the conditions of his student visa due to his "political activities outside the campus," and must therefore leave the country.
During the meeting, Lindenthal said, he was asked for his views on the protests against the new Indian law, which grants citizenship to non-Muslim religious groups fleeing persecution from three Muslim-majority countries.
"I think nobody can claim that I was just there to exploit my student visa to go on anti-government demonstrations and harm the country's integrity or something. But that was how they presented it to me," said Lindenthal, who spoke to Reuters from New Delhi while awaiting a Christmas day flight back to Germany.
India's Home Ministry did not immediately respond to a request for comment, while a spokesman for the foreign ministry declined to comment.
The Indian Express newspaper quoted an official at India's Foreigners Regional Registration Office as saying that while he was unaware of Lindenthal's case, it appeared to be a "clear case" of violating visa rules.
Indian opposition leaders, who accuse Modi's Hindu nationalist government of strong-armed tactics to muzzle dissent, decried Lindenthal's expulsion.
"This is dismaying. We used to be a proud democracy, an example to the world... No democracy punishes freedom of expression," tweeted Congress lawmaker Shashi Tharoor.At Pondicherry University in southern India, four students boycotted the graduation ceremony on Monday and one refused to accept her gold medal in protest at the citizenship law, according to student council president Parichay Yadav.