The police said Krishna Mohan Shrestha was killed outright while walking near his house on the outskirts of the city. His wife, Nudup, and bodyguard were also killed.
They said that the three were repeatedly shot by several assailants who got away. No arrests have been made yet.
The BBC's Daniel Lak in Kathmandu says if Maoist involvement is confirmed, Mr Shrestha will be the highest-ranking official deliberately targeted by the insurgents.
Our correspondent says that the use of assassination as a tactic has been rare and will be seen here as a significant escalation in the conflict.
Failed peace talks
Nepal's armed police force was formed about two years ago to combat Maoist rebels, who are waging a violent campaign to turn the Himalayan Kingdom into a communist state.
Violence between the rebels and Nepalese security forces has intensified after failed peace talks last year.
Much of the countryside is either under Maoist control or not actively patrolled by the army or the police.
Correspondents say it is rare for the rebels, who often target remote police camps, to strike in the capital.
The rebellion has destabilised the political situation in Nepal and all but wrecked a once thriving tourist economy.
The United States has established a $17 million military assistance fund to help the government fight the insurgents.
The Nepalese Government says the insurgence has killed more than 7,000 people, most of them suspected Maoists or civilians.
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