The Videocon Group chief Venugopal Dhoot has also been summoned in the same case.
On Friday, the ED had searched premises of Chanda Kochhar and Venugopal Dhoot in Mumbai and Aurangabad respectively in connection with a money laundering case, an official said.
The development comes weeks after the ED registered a criminal case against the two for alleged money laundering. The case was registered under the Prevention of Money Laundering (PMLA) Act.
On February 22, the Central Bureau of Investigation (CBI) had issued lookout circulars (LOCs) against Kochhar, her husband Deepak Kochhar and Videocon Group's Managing Director Dhoot.
"The LOCs were issued after the FIR was filed in the case. LOCs are mandatory in cases where such economic offences are alleged," the official said, adding, "In recent times, keeping an eye on travel plans is a top concern for regulators."
The ED had registered a criminal case last month against Kochhar, her husband, Deepak Kochhar, Venugopal Dhoot and others to probe alleged irregularities and corrupt practices in sanctioning of an Rs 3,250-crore loan by the bank to the corporate group.
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The CBI had filed a complaint last month and an Enforcement Case Information Report later under the PMLA.
The agency is probing if alleged kickbacks were generated in the loan deal and laundered to create tainted assets.