On Tuesday, Jersey Police searched premises suspected to be connected to Mr Abramovich's business activities on the island, Jersey Law Officers' Department said.
The billionaire is on the UK sanctions list over Russia's war in Ukraine.
Channel Island Jersey follows UK policy and imposes sanctions on the same people.
"The Royal Court also imposed a formal freezing order on 12 April, known as a saisie judiciaire, over assets understood to be valued in excess of US$7bn which are suspected to be connected to Mr Abramovich and which are either located in Jersey or owned by Jersey incorporated entities," the Jersey Law Officers' Department said.
Mr Abramovich was among several wealthy Russians added last month to the UK and European Union sanctions lists over Russia's invasion of Ukraine, and governments have since been taking action to seize yachts and other luxury assets from them.
The billionaire tried to sell Chelsea Football Club in March, but that process was taken out of his hands by the government after he was sanctioned.
Earlier this month, the Caribbean nation Antigua and Barbuda said it was willing to help the UK seize yachts owned by Abramovich.
Superyachts linked to the businessman, together worth an estimated $1.2bn, have also been docked in southwest Turkey, outside the jurisdiction of the EU and the UK, BBC reports.
