The central probe agency said it seized mutual funds of Whitefield Chemtech Private Limited, "which is controlled by Amin and his family", under section 37A of the Foreign Exchange Management Act (FEMA).
The names of Mr Amin and his family members, it said in a statement, had figured in the Panama Papers case with respect to their stakes/interests in the firm in the British Virgin Islands.
During the investigation, the agency said, it was noticed that Mr Amin and his family members, through their company Whitefield Chemtech Pvt Ltd India, had "invested an amount of USD 1.6 million for purchase of a 3BHK apartment in Campden Hill, UK".
"For purchase of this property in the UK, the firm transferred an amount of $ 2.4 million to its subsidiary in Singapore in the form of overseas direct investment.
"This amount was further transferred to its step-down subsidiaries in the UAE and British Virgin Island from where finally $ 1.6 million was used for purchase of this property," the ED said.
Section 37A of the FEMA stipulates that if certain foreign exchange, foreign security or immovable property is held outside India in violation of this law, the equivalent value of asset can be seized within India.
"Accordingly, equivalent asset amounting to Rs 10.35 crore in the form of mutual funds were seized under Section 37A of FEMA, 1999," it said.
The agency is probing the Indians named in the Panama Papers, along with the Income Tax Department.
The Panama Papers, that surfaced last year, contained brief particulars of about 426 people, prima facie, Indians or persons of Indian origin.
The government had constituted a multi-agency group (MAG) of investigative agencies in April 2016 to probe these instances.
The MAG has so far submitted seven reports to the government.
Mr Amin was chairman of Indian Premier League (IPL).