The minister, Pankaj Chaudhary, did not name which companies were involved.
Shares of Adani group companies, which operate airports and ports, power generation and transmission, coal and gas trading, closed between 1.1%-4.8% lower on Monday.
"SEBI is investigating some Adani Group companies with regard to compliance with SEBI Regulations. Further, the Directorate of Revenue Intelligence (DRI) is investigating certain entities belonging to the Adani Group," Chaudhary said.
Stocks of companies controlled by Indian billionaire Gautam Adani last month recorded their biggest-ever declines in the week ending June 18, after Indian newspaper Economic Times reported the accounts of three Mauritius-based foreign investors in Adani companies had been frozen.
Shares in the six Adani companies have fallen between 12.9%-44.9% in the five weeks after the Economic Times report.
The stocks have cumulatively lost over $37.6 billion in just over a month after the Economic Times report, even after Adani rejected the article as "blatantly erroneous."