Paris police spokeswoman Johanna Primevert told The Associated Press that the attacker targeted officers guarding the area near the Franklin Roosevelt subway station at the center of the avenue popular with tourists. She said he appeared to be acting alone.
Police and soldiers sealed off the area, ordering tourists back into their hotels and blocking people from approaching the scene. The Paris prosecutor's office said counterterrorism investigators are involved in the probe.
French Interior Ministry spokesman Pierre-Henry Brandet said on BFM television that a man came out of a car and opened fire on a police vehicle. He said officers were "deliberately" targeted.
Speaking in Washington during a news conference with Italian Prime Minister Paolo Gentiloni, U.S. President Donald Trump said the shooting in Paris "looks like another terrorist attack" and sent condolences to France.
Emergency vehicles blocked the wide avenue that cuts across central Paris between the Arc de Triomphe and the Tuileries Gardens, normally packed with cars and tourists. Subway stations were closed off.
Security forces are more widespread in Paris since deadly Islamic extremist attacks in recent years, and France remains under a state of emergency.
Thursday's attack came three days before the first round of balloting in France's tense presidential election. Security is high preceding the vote after police said they arrested two men Tuesday in what they described as a thwarted terror attack.
French President Francois Hollande scheduled an emergency meeting Thursday night.
The incident recalled two recent attacks on soldiers providing security at prominent locations around Paris, one at the Louvre museum in February and one at Orly airport last month.
A witness identified only as Ines told French television station BFM that she heard a shooting and saw a man's body on the ground before police quickly evacuated the area where she works in a shop.
A French television station hosting a televised event with the 11 candidates running for president briefly interrupted its broadcast to report the shootings.
None of the candidates immediately commented.