Speaking during his poll campaign tour of Gujarat, he claimed that the share market regulator has termed Mr Rupani "beimaan" (dishonest) and imposed fine on him.
Mr Gandhi asked Prime Minister Narendra Modi to speak out on this issue.
"Gujarat is more corrupt than the entire country. Surat businessmen told me that policemen come to their units every two minutes (allegedly to demand bribe)," he said.
The 47-year-old Congress leader was addressing a public meeting in the Banaskantha district on the second day of his campaign tour of North Gujarat.
"Jay Shah, son of (BJP chief) Amit Shah, increased the turnover of his company from Rs 50,000 to Rs 80 crore in a few months after the BJP came to power in 2014. The people of Gujarat know this cannot be done without corruption," he said.
"Some days ago, the SEBI said your chief minister is beimaan (dishonest) and they fined him. Modiji used to say 'na khaoonga, na khane doonga' (I will neither take graft nor allow corruption). Please open your mouth on this subject now. But he is silent. Now his slogan is 'na bolta hu, na bolne dunga' (I will not speak myself and won't allow others to do so')," Mr Gandhi said.
"The people of the country want to listen what you (Modi) have to say on Amit Shah's son's company, on Vijay Rupani. The people of Gujarat will believe that you are not 'chowkidar' (watchman) but 'bhagidar' (collaborator) if you don't say anything on the issue," he said.
The Securities and Exchange Board of India (SEBI) has reportedly fined 22 entities, including Rupani HUF (Hindu Undivided Family), for alleged manipulative trading in the shares of a company, Saran Chemicals Ltd, during the January-June 2011 period.
However, Mr Rupani had said the Securities Appellate Tribunal (SAT) has set aside the fine of Rs 6.91 crore imposed on 22 entities, including his firm.
The fine amounts varied for the entities and it was reportedly Rs 15 lakh in the case of HUF of Mr Rupani, who took over as the Chief Minister in August 2016 and is currently in the thick of the BJP's campaign for the next month's assembly polls.