The attack on Thursday was the first on security forces since the rebels ended a four-month truce this week, police said.
The shooting took place in the town of Mahendranagar, the largest in the district of Kanchenpur, a rebel stronghold 650km west of the capital, Kathmandu.
“Eight police officers were on their way to replace their colleagues when the Maoists fired on them,” a police officer said.
One officer was hit in the stomach and the other in the chest. A 62-year-old passer-by was also wounded.
On Monday, the rebels ended a four-month unilateral ceasefire, accusing government forces of provoking the move.
They have been fighting since 1996 to topple the Hindu monarchy and set up a single-party communist state.
The government said troops were on alert across the country to avert further attacks by the Maoists.
The interior ministry said soldiers had been ordered to carry out searches in Kathmandu after the recent seizure of arms hidden in the city.
The government vows to crush the insurgency, which has killed more than 12,500 people.