The police department tweeted a warning Monday without providing further details. The high-end neighborhood is popular with tourists.
The reason for the operation remains unclear.
A subway station in the area is closed.
An attacker defending the Islamic State group shot and killed a police officer on the Champs-Elysees in April, days before a presidential election, prompting an extensive security operation. France is under a state of emergency after a string of deadly Islamic extremist attacks.