Shares in India's biggest property developer DLF Ltd
Vadra and DLF have denied the allegations.
DLF shares were down 6.4 percent as of 1:07 p.m., after falling as much as 6.9 percent. The Sensex declined 0.8 percent.
Activist Arvind Kejriwal, along with colleague Prashant Bhushan from their anti-graft group India Against Corruption, accused DLF on Friday of arranging favourable loans and real estate transactions for Vadra.
The claims were detailed in a document posted on the group's website.
"We would like to state that the business relationship of DLF with Mr Robert Vadra or his companies has been in his capacity as an individual entrepreneur, on a completely transparent and at an arm's length basis," DLF said in a statement on Saturday.
"Our business relationship has been conducted to the highest standards of ethics and transparency, as has been our business practices, all around."
Vadra also issued a public statement calling the activist accusations "utterly false, entirely baseless and defamatory."
The businessman condemned what he said were attempts to "deliberately misrepresent numbers contained in my financial statements, manufacture lies and malign my family in order to gain cheap publicity for them and for the launch of their political party".
Sonia Gandhi has no official government post but is the Congress party president and powerful matriarch of India's widely revered first family. She is known to play a major role in decision-making on big policy issues.