An eyewitness said residents in Galle, a city which was devastated by a tsunami in 2004 were rushing to safety, some were crying and there were traffic jams.
Hawaii's Pacific Tsunami Warning Centre has said an earthquake of 8.7 magnitude had occurred off the coast of Northern Sumatra in Indonesia generating a tsunami but wave action monitored so far were around a foot in Indonesia.
However local conditions could create variations in the size of the waves, a second wave could be higher, the PTWC said. It took about two hours after the estimated time of wave arrival for the danger to pass completely.
The PTWC earlier said waves are expected to reach Sri Lanka's coast in Trincomalee at 4.19 pm hours (1039 GMT) can the capital Colombo by 04.51pm.
Waves would reach Dondra in the South coast at 04.24 pm and Jaffna in the north at 6.05 pm.
Residents in several parts of Sri Lanka reported feeling the quake.
In December 2004 an tsunami from a much larger quake (9.6 on the Richter scale) devastated large parts of Sri Lanka.
A magnitude of one indicates an increase in the size of the earthquake by 10 times..