Lieutenant-General Parami Kulatunga, the deputy chief of staff, was travelling to a military base when motorcyclists approached his convoy about 20km (12 miles) east of Colombo on Monday.
Chaminda Banunurachchi, chief inspector of police, told Reuters at the scene: "The general is dead. Two others are also dead. I think it was a suicide attack by motorcyclists against the general."
Military sources had earlier said that four people were killed in the attack in the town of Pannipitiya, about 10km from a large army base; but Banunurachchi said the death toll was three.
The Tamil Tigers had no immediate comment on the incident, but routinely deny involvement in attacks.
A Reuters witness at the scene saw a burnt-out Peugeot car on the road still smouldering. Another pick-up truck in the general's convoy was damaged.
The attack comes after a number of ambushes and military clashes that have killed about 700 people - half of them civilians - so far this year.
Many fear the rise in violence could re-start a two-decade civil war with the rebels.