Wearing the diamond could remind people of the British Empire, a spokesman for Indian Prime Minister Narendra Modi’s political party is reported as saying.
Camilla's priceless crown features 2,800 diamonds, with the front cross holding the famous 105-carat Koh-i-Noor diamond, one of the largest cut diamonds in the world.
The crown was originally made in 1937 for Queen Elizabeth, consort of King George VI, using many stones already in the royal collection.
Most of them were removed from Queen Victoria's Regal Circlet.
The Koh-i-Noor diamond was also mounted in the crowns of Queen Alexandra and Queen Mary..
Queen Elizabeth wore the crown without its arches at the State Openings of Parliament during the reign of King George VI, and again at the coronation of her daughter, Queen Elizabeth II, in 1953.
Koh-i-Noor - in pictures
The origins of the diamond are not known, although there is no doubt that it was panned in India. The earliest reference appears to relate to a powerful Mughal ruler in 1628.
The stone returned to India in 1813 and become a potent symbol of power until it was acquired by Britain in 1849.
It was given to Queen Victoria in 1855 by 10 year-old Duleep Singh, last emperor of the Sikhs.
Although much has been made of the fact that it was "given" to Britain, critics say this was only after the mother of the heir to the Punjabi throne was held prisoner and forced to sign it away.
It then became a special possession of Queen Victoria and was displayed at the 1851 Great Exhibition in London.
Since then it has become part of the Crown Jewels, and a point of dispute between the UK and India, and several other nations, ever since.
The Koh-i-Noor: What is the controversy? - video
William Dalrymple, who co-wrote Koh-i-Noor: The History of the World's Most Infamous Diamond with colleague Anita Anand, said: "It is not a small sensitive issue in the eyes of India.
"It is a massive diplomatic grenade.
"One of the reasons we wrote our book was that we don't believe anyone in this country has the slightest conception of how much it matters in India.
"For people here it is the name of an Indian restaurant or a brand of pencils, or maybe something they have seen on a school trip to the Tower of London.
"But it is actually part of a wider disconnect of a number of things that Indians get very upset about to do with the colonial period.
"It matters to a huge number of people and has continued to be very controversial since the queen died.
"There is an expectation that this is an issue that will come back. Colonialism is over. Britain wants to make friends with India. It is a major new rising power.
"In a sense the British have brought this on themselves because they turned the stone into a symbol of their empire by putting it on display in the Great Exhbition of 1851.
"It has [since] become, rightly or wrongly, a symbol for many colonised people of all they think that we took from them. Whatever your position on it, that is how it's viewed.
"This tiny stone, which is actually not that big — in fact, and it's not even in the top 100 of the world's diamonds any more — has come to take the whole weight of colonisation on its shoulder.
"It has become this very, very sensitive object and is a major issue now between the two countries."
Queen Elizabeth's jewellery goes on display for Jubilee - in pictures
Camilla is due to be crowned in a simpler ceremony as part of King Charles III’s coronation on May 6 next year in Westminster Abbey.
“The coronation of Camilla and the use of the crown jewel Koh-i-Noor brings back painful memories of the colonial past," a spokesman for Mr Modi’s Bharatiya Janata Party told The Telegraph.
“Most Indians have very little memory of the oppressive past. Five to six generations of Indians suffered under multiple foreign rules for over five centuries.
“Recent occasions, like Queen Elizabeth II’s death, the coronation of the new Queen Camilla and the use of the Koh-i-Noor does transport a few Indians back to the days of the British Empire in India.”
The gem, which is held in a detachable platinum mount, may now be taken out of the crown before use.
The crown might not even be used at all if Camilla favours something simpler, such as Queen Victoria's coronet.
Buckingham Palace declined to comment when asked about the remarks.
Famous jewels and the women who have worn them - in pictures
The palace said the ceremony would be “rooted in longstanding traditions and pageantry”, but also “reflect the monarch’s role today and look towards the future”.
King Charles will be anointed with holy oil, receive the orb, coronation ring and sceptre, be crowned with the majestic St Edward’s Crown and blessed during the historic ceremony.
Camilla will also be anointed with holy oil and crowned, just like the Queen Mother was when she was crowned in 1937.