Cracks - thought to be caused by persistent rain -  began to appear on Old Beer Road in Seaton on Wednesday.
Within 48 hours part of the road had collapsed and Devon County Council is now concerned more of the road could disappear.
The South West Coast Path is being diverted from the route and diversion signs put in place.
Members of the public have been urged to stay away from the "potentially dangerous" road.
Bob Spalding, who lives in Seaton, uses the road every day to walk into Beer.
He contacted the council after noticing hairline cracks on Wednesday, which he photographed.
"The next day the cracks were alarmingly worse and you can see by today's photograph what has happened since," he said.
"Fortunately it's no longer the main road, but is mainly used by local people going to Beer."
Mr Spalding said the road was only resurfaced a few months ago, which is why the signs of erosion were so visible.
The council said the road had dropped by about 1m (about 3ft) in the past 24 hours and barriers had been put up to prevent any access.
Councillor Stuart Hughes, the council's highways and transportation cabinet member, said: "This section of road is moving and is potentially dangerous so I would ask people to steer clear and please respect the barriers that are there for your safety.
"The road will remain shut while we assess how much more of the road could move, but if the wet weather continues further damage could be caused so it is not safe for people to get too close."
A road in Devon has been closed indefinitely after part of it collapsed.