Police said they feared casualties as flash floods swept through villages who were totally unprepared, but there was no immediate count on casualties.
The waves came after a powerful earthquake in the Indian Ocean that struck Indonesia, about 1,400 kilometres (875 miles) away.
Hundreds of villages along the island's eastern and southern sea board as well as towns along the southern coast were battered with many houses completely destroyed, police said.
"The police station is also under water here," an officer in Matara, 160 kilometres (100 miles) south of here said by telephone.
Tourist resorts along the coast said they were badly hit with almost all of them flooded.
Reports from the coastal area suggested that a stretch of over 700 kilometres from Trincomalee in the island's east to Kalutara in the south had been hit by huge tidal waves.
The massive waves were moving northwards and heading towards the coastal capital of Colombo.