The road side blast targeting a police vehicle was caused by a Claymore-type bomb at Ottamawadi in the district of Batticaloa, a police official said by telephone.
"Two civilians and a constable were killed on the spot," the officer said from the nearest town, also called Batticaloa, 300 kilometres (187 miles) east of the capital.
"Another 10 civilians, four constables and two soldiers escaped with injuries," he added.
Police said they believed the rebel Liberation Tigers of Tamil Eelam (LTTE) were behind the latest bomb attack in the restive eastern coastal district.
There was no immediate comment by the LTTE on the attack, which came on the eve of the fifth anniversary of a truce arranged and put in place by peace broker Norway.
Ceasefire monitors say the truce holds only on paper.
Over 60,000 people have been killed in Sri Lanka's Tamil separatist conflict in the past 35 years. An escalation in violence since December 2005 has left nearly 4,000 people dead.