The storm had weakened from a Category Four to a Category Three, but still had maximum sustained winds of more than 205km/h (125mph).
Teams are out clearing roads and repairing buildings and power lines.
Last week Hurricane Matthew devastated parts of Haiti, killing hundreds of people.
"At this point, there is no indication of any loss of life or serious injuries," Premier Michael Dunkley told Reuters news agency.
"Nicole is now racing away,'' said James Dodgson, deputy director at the Bermuda Weather Service.
