The British Geological Survey is investigating a magnitude 4.1 earthquake that was recorded under the Bristol Channel.
Julian Bukits, from the society, confirmed the earthquake occurred at approximately 1.21 pm and had a depth of 3.1 miles.
He said the society is analysing the earthquake to measure its size.
The BGS said residents reported their houses rocking, while others compared the tremor to a "heavy truck going up the road".
Tremors were felt in areas including Dartmoor, Bristol, Taunton, Swansea, Llanelli, Barnstable, Gloucester and South Molton.
A BGS spokesman said: "At this time the BGS have received several macroseismic reports from residents throughout Devon and South Wales.
"One describing 'the house was rocking', another described 'lasted several seconds and it was very frightening' and another said 'it felt like a really heavy truck going up the road'."
The ground shook in the area for around 10 seconds and has been felt as far as Swansea and Devon.
The National Trust Gower tweeted: "Just experienced what seemed like an earthquake! Anyone else?"
Ant Veal tweeted: "Noticeable earth tremor just now (13.22GMT) in Exeter. Lasted 3 seconds.
Gareth Jones in east Devon tweeted: "Whole floor at work just felt a wobble! Tweets across sw of england/wales reporting something?"