Nirav Modi, a diamond broker and luxury jeweller to celebrities, is being investigated in a $44m (£31m) fraud case at Punjab National Bank (PNB).
Late on Friday, India’s federal police arrested two bank officials and a business associate of Mr Modi’s.
Mr Modi has not yet commented on the case, and no charges have been filed.
PNB has also claimed Mr Modi is involved in a $1.8bn (£1.3bn) fraud. That amount is almost a third of the bank’s market value, and many times its quarterly profits.
Nirav Modi is one of India’s richest people, with a personal wealth of $1.75bn, according to Forbes.
He has also been the jeweller for celebrities such as Naomi Watts and Kate Winslet – while one of India’s biggest stars, Priyanka Chopra, is his company’s brand ambassador.
While no charges have been brought against Mr Modi, police have conducted several high-profile raids of his luxury jewellery shops.
India’s Central Bureau of Investigation (CBI) named the three arrested as former deputy manager Gokulnath Shetty, Manoj Kharat, and Hemant Bhat, Mr Modi’s associate.
A spokesman told the AFP news agency that Hemant Bhat was the “authorised signatory” of several companies linked to Mr Modi.
The three are jointly suspected of making fraudulent lines of credit available to companies linked to Mr Modi and his uncle, Mehul Choksi, the spokesman said.
Mr Choksi is head of the Gitanjali Group, which has about 4,000 shops across India.
PNB said a series of transactions at a single branch in Dubai were made “for the benefit of a select few account holders with their apparent connivance”.
Many reports say Mr Modi has left the country, and police have as yet been unable to speak with him.
Both Mr Modi and his uncle have had their passports suspended.
A spokeswoman for India’s tax authority told Reuters it had seized 105 bank accounts and 29 properties linked to Mr Modi and his companies, as it investigates possible tax evasion.
Meanwhile, opposition political parties have been seeking to link Mr Modi to Prime Minister Narendra Modi after a photo emerged of the pair together at the World Economic Forum in January – along with dozens of others. The men are not related.
Nirav Modi was born into a diamond trading dynasty, based in the industry capital Antwerp, and later established Firestar Diamond – his own diamond making operation in India almost 20 years ago.
He started trading under his own name in 2010, specialising in diamonds.
The brand made its mark in some style after one of his earliest pieces was featured on the front cover of a Christies catalogue and was sold by the auction house in Hong Kong for $3.8m.