Mr Bush has been in power since his United Democratic Party (UDP) won general elections in 2009.
The British overseas territory is one of the world’s largest financial centres and a well-known tax haven.
On its website, the Royal Cayman Islands Police Force said: “The Premier of the Cayman Islands, McKeeva Bush (57), has been arrested and is currently detained in police custody in connection with a number of ongoing police investigations.”
Mr Bush previously held the post of leader of the islands’ government between November 2001 and May 2005.
A member of the legislative assembly representing West Bay, he also holds the post of minister of finance, tourism and development.
(Reprinted from BBC News)