The bomb is reported to have gone off near a school in a residential area of the city.
Police say the target may have been a Tamil politician opposed to the Tamil Tiger rebels.
The blast comes as the Tigers and military continue heavy fighting in the north-east of the island.
"The blast was near St Paul's College. It was a van," a military spokesman told the Reuters news agency.
A witness told the agency that one of the dead was a child.
People nearby said they could see plumes of smoke rising above the scene of the blast.Güncelleme Tarihi: 20 Eylül 2018, 18:16