Researchers found residues of potassium bromate and potassium iodate in 84% of the samples collected from Delhi.
The chemicals are banned in many countries, but India continues to allow their use in bakeries.
The All India Bread Manufacturers' Association said the chemicals were "considered safe".
Health Minister JP Nadda has urged people  not to panic and to wait for his ministry's report on the issue.
"I have told my officials to report to me on an urgent basis. There is no need to panic. Very soon we will come out with the [inquiry] report," he said.
Delhi-based environmental think-tank Centre for Science and Environment (CSE) said in its report that it had collected 38 bread and bakery samples from retail stores, bakeries and fast-food shops in Delhi for its study.
"More than 84% of samples tested were found to contain potassium bromate and/or iodate," it said.
The CSE has urged the government to ban the use of these chemicals in bakery products.
"Considering that it [potassium bromate] can cause cancer, is banned in most parts of the world, and has healthy alternatives, there is no reason why this chemical should be allowed, specifically when residues are found to be present in the end-product."
The CSE said potassium iodate should also be banned because "it can potentially affect the functioning of thyroid".
The bread manufacturers' association said it was yet to see the CSE report, but added that the two additives were safe and "widely used in advanced countries like the US".
"Food Safety and Standards Authority of India's regulations permit the use of potassium bromate and/or potassium iodate at 50 ppm max for bread and at 20 ppm max for bakery purpose," the association said in a statement.
India's health ministry has ordered an inquiry after a study found cancer-causing chemicals in many bread and other bakery products.