Mr Aich died of age-related "complications" on Sunday, his family said. He is survived by four children.
Mr Aich was the first Indian to become Mr Universe in 1952, five years after the country's independence.
The 1.49m (4ft 10in) tall bodybuilder was popularly known as "Pocket Hercules".
He began his career as a stunt man performing with a famous magician and would often enthral the audience by bending steel with his teeth or resting his belly on swords.
Mr Aich, who once stood for election and lost, gave his last performance at the age of 89.
"He was an inspiration to everyone, young and old. Death is inevitable but Manohar Aich will be remembered by all, across every sporting discipline," footballer Chuni Goswami told The Indian Express newspaper.
India's centenarian Mr Universe
West Bengal Chief Minister Mamata Banerjee said Mr Aich's death had "ended a historic era".
"He made us proud," Ms Banerjee said.
After getting a job as a physical instructor in the Royal Air Force in British India in 1942, Mr Aich led his team to rebel against what he felt was the "oppression" of their British commanders.
An argument ensued and Mr Aich ended up slapping a British officer, for which he was sent to a Calcutta jail a year before India achieved independence from British rule in 1947.
With little else to do in jail, Mr Aich practiced his metal-bending skills on the bars of his cell.
After the triumphs of his youth he continued to display his strength at shows across India and is credited with inspiring millions of Indians to get fit.
When Mr Aich competed in the 1952 Mr Universe contest in London, his statistics were awe-inspiring: bicep 46cm, chest 1.2m when swollen, forearm 36cm and wrist 16.5cm.
"I have been blessed with this body," he told the BBC in 2012. "What else does one want?"
Tributes have been paid to a celebrated Indian body-builder, Manohar Aich, who has died in the city of Kolkata (Calcutta), aged 104.