The man, who has not been named, will be referred to a parish hall inquiry to decide whether he should be charged and sent to court.
The force said the alleged offences fall under the Telecommunications Law.
In a brief statement, the force said: ‘Following some grossly offensive comments made on social media recently concerning visiting refugees, a 55 year old man has been arrested for offences under the Telecommunications Law.
He has been reported for consideration of the question of prosecuting him and will appear at a parish hall inquiry in the coming weeks.’
Earlier this week the force announced it was investigating comments online made in relation to the visit of three refugees to take part in a play at the Jersey Arts Centre.
