The quake, measuring 5.6 on the Richter scale, hit at 11:25 am (0825 GMT) and was followed by 10 aftershocks before midday, the island's geological survey department said.
The epicentre was off the resort of Paphos on the island's southwest coast but it was felt in the capital Nicosia 110 kilometres (70 miles) away.
There were no immediate reports of casualties or serious structural damage.
But police said they had received some reports of falling debris and authorities were still assessing the damage.
Wednesday's quake at a depth of 25 kilometres (15 miles) under the sea was the strongest since another 5.6-magnitude quake in 1999.
The biggest quake ever recorded on the island was a 6.5-magnitude tremor in 1996 which claimed two lives and damaged buildings in both Paphos and the island's second city Limassol.