Jersey's Minister for Children and Education Jeremy Macon has been relieved of his duties following his arrest.
Chief Minister John Le Fondre said Deputy Macon is "not currently capable of fulfilling his duties".
States of Jersey Police said a 33-year-old man was arrested at a private address and has been released on bail pending further inquiries.
Police and the Government of Jersey declined to comment on the arrest.
Senator Le Fondre confirmed he had removed Mr Macon's ministerial duties and taken over his portfolio personally "until further notice".
"To respect the privacy of all individuals concerned, no further details will be shared at this stage", he added.