The bombing in Colombo's Pettah area came a day after Tiger rebels accused government forces of setting off a roadside bomb and killing two civilians inside guerrilla-held territory.
A man and a child died when their motorcycle was caught up in the bomb attack at Nedunkerni in the vast Wanni region on Thursday evening, the LTTE said in a statement on Friday.
The military routinely denies that it carries out attacks against civilians inside Tamil Tiger-controlled areas.
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It is impossible to verify independently casualty figures as the government bars access to the front-lines by journalists and rights groups.
UN aid agencies say nearly 135,000 people have been driven from their homes due to fierce fighting in the past two months.
Sri Lankan troops have been pushing deeper into rebel-held territory as they try to dismantle the LTTE's northern stronghold.
They ejected the guerrillas from the east of the island in July 2007.
Tens of thousands have died on both sides since