The gunman also wounded two police officers before he was killed by security forces on the Champs-Elysees.
President François Hollande is to chair a security cabinet meeting, as France readies for Sunday's presidential poll.
Mr Hollande said he was convinced the attack was "terrorist-related", adding that the security forces had the full support of the nation and a national tribute would be paid to the fallen policeman.
So-called Islamic State (IS) said one of its "fighters" had carried out the attack.
A car pulled up alongside a police bus just before 21:00 (19:00 GMT) and a man got out, opening fire on the bus with an automatic weapon, Interior Ministry spokesman Pierre-Henry Brandet said.
After killing an officer, the man attempted to run away while shooting at other officers, two of whom he injured, the spokesman added.
He was then shot dead by security forces.
Terrified eyewitness later recounted scenes of panic as they ran for cover after hearing gunfire.
The whole of the Champs-Elysees was evacuated.