Howling winds and rough seas battered the British overseas territory, experiencing a top-rated category five hurricane for the first time.
There has been some damage and flooding in Haiti, which is still recovering from the devastating 2010 earthquake.
Some 500,000 people were told to leave south Florida with Irma due on Sunday.
The hurricane's winds have moderated slightly, at up to 270km/h.
An estimated 1.2 million people have been affected by Irma and that could rise sharply to 26 million, the Red Cross says.