Crews were called to La Corbière on Sunday afternoon.
All emergency services were understood to be dealing with the incident close to the lighthouse.
It is believed a car went over the cliff edge and landed on its roof.
States of Jersey Police said the road remained open but asked people to avoid the area.
Storm Benjamin dramatically ends Guernsey's dry spell
Winds were generally mid Channel but hit 80 mph overnight at St Helier harbour.
No main roads blocked following Storm Benjamin
All main roads remain passable this morning as teams undertake clear up.
New housing in St Helier will now need to come with a parking space
Politicians have approved calls for all new housing developments in St Helier to provide at least one parking space for every flat or house.
Red warning issued for severe winds
A red level wind warning has been issued for the Channel Islands, with F8 gales forecast.
Water levels still low despite October rainfall
Water levels in Jersey's reservoirs remain low, despite the recent rain.
Constable's attempt to extend Millennium Town Park fails
Jersey's government will press on with plans to build a new primary school on the former gasworks site.
JSPCA shares 'huge concern' for future of its charity shop amid St John road closures
The JSPCA charity shop is calling for support in the run-up to 15 months of roadworks on St John's main road.
Inspectors find inclusion for SEND children is lacking
Inclusive teaching for children in Jersey with Special Educational Needs and disabilities (SEND) is lacking, independent inspectors have found.
