The blast occurred during morning rush hour directly in front of the police building in Vavuniya town, 258 kilometres (160 miles) north of Colombo, military and police officials said.
The wounded, who included school children, were rushed to the main hospital.
"It was a Tiger suicide bomber who rammed his (explosives-packed) motorcycle as policemen were leaving for duty," military spokesman Udaya Nanayakkara said.
Nine policemen and three female constables were killed while another 17 policemen were wounded, police spokesman Ranjith Gunasekara said.
"All those killed in the attack were police personnel," Gunasekara said adding, however, that civilians were among the wounded.
The most senior police official was not in the building at the time of the blast, a policeman in Vavuniya said when contacted by telephone.
Officials at the Vavuniya hospital said they had received the bodies of 12 people killed in the blast, and a further 40 were rushed in for treatment.
Vavuniya