Inaugurating the new headquarters of the National Investigation Agency here, the minister said such allegations are levelled "from time to time".
"Such allegations have surfaced in the past too. They are levelled from time to time. It has no basis," he told reporters on the sidelines of the function.
News portal The Wire reported that a firm owned by Shah's son Jay Amit Shah saw a huge rise in turnover after the BJP came to power in 2014.
The charge has been rejected by the BJP and Shah's son, who termed the report "false, derogatory and defamatory".
The Congress is asking Prime Minister Modi to remove Shah as the BJP chief and order a probe by Supreme Court judges.
Jay Shah yesterday filed a defamation case in an Ahmedabad court against news portal 'The Wire' over the report.