The bomber on the motorbike hit the bus carrying police personnel near Sambuddhaloka Viharaya at the fort area, the Defence Ministry said.
The blast came a day after officials said that at least 31 Tamil Tigers and five soldiers were killed in fresh clashes in Sri Lanka's embattled northern region.
Among the 10 dead in the blast were eight police personnel, three of them women, a ministry official said, adding 86 people, including 50 civilians, were also injured.
Condemning the blast, Sri Lankan President Mahinda Rajapaksa described it as the "latest act of cowardice and brutality by the LTTE."
"Repeated savagery of this order underlines and reiterates the need for concerted action by all those who cherish democracy, human rights and the values of civilised society, to eradicate the menace of terrorism of which the LTTE remains the bloodiest example today," Rajapaksa said.
Panic-stricken people were seen running around after the blast, with several blood-soaked bodies lying on the ground.
The police patrol personnel rushed the injured to hospitals. Director General of the National Hospital, Hector Weerasinghe, said several injured have been admitted to the medical facility.