The officer, 24, lost control of the car and drove it into a sandbox in the western city of Lutsk, the Interior Ministry said.
A 3-year-old girl and a 4-year-old boy died at the scene, and a 5-year-old boy was hospitalized with multiple injuries, the ministry said. It said the policeman was also injured and hospitalized.
The ministry did not specify whether the policeman was on duty at the time and whether he was driving his own car or a police vehicle. Officials could not immediately be reached for comment.
Drunkenness and alcoholism continue to plague countries in the former Soviet Union, contributing to high road accident rates and overall death rates.