A portrait of India's founding father was also vandalised with the word "deshdrohi" (traitor) scrawled across it in green paint.
For most, Gandhi is the father of the nation, but some Hindu hardliners view him as a traitor for his advocacy of Hindu-Muslim unity and for the division of India.
The incident comes as India celebrates the 150th birth anniversary of the independence hero.
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"I opened the gate of the Bhawan early in the morning because it was Gandhi's birthday," said the caretaker of the Bapu Bhawan memorial, Mangaldeep Tiwari.
"When I returned at around 11 pm, I found the mortal remains of Gandhi missing and his poster was defaced," he added.
The police took action after a leader of the Indian Congress party filed a complaint.
The remains of Gandhi have been kept in the memorial since January 1948 when he was assassinated by a Hindu extremist.
Earlier in February, a right-wing Indian leader shot an effigy of independence hero Mahatma Gandhi with an air pistol to mark his assassination some seven decades ago.
Pooja Shakun Pandey was filmed shooting the effigy at an event by a far-right Hindu group on the 71st anniversary of Gandhi’s death. The video sparked anger after going viral online.
Gandhi was assassinated on January 30, 1948 by Nathuram Godse, a Hindu fanatic angered by what he saw as Gandhi’s pandering to Muslims and by the partition of India after independence.
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