Col. John Fortunato, a Jefferson Parish Sheriff's spokesman, announced the officer's death as police flooded the area, searching for the suspect by helicopter and combing the area with dogs.
The deputy was not identified. The deputy was pronounced dead after being rushed to University Medical Center in New Orleans.
The reason the pedestrian was stopped was not immediately available, and it was unclear what prompted the shooting.
Fortunato said Sheriff Newell Normand was out of town but planned an immediate return and scheduled a 10 PM news conference on the shooting.
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It was the year's second shooting of a Jefferson officer. Another member of the Jefferson Parish Sheriff's Office was shot and wounded in January during a drug raid on a house in the Lower 9th Ward section of New Orleans.
Stephen Arnold was shot five times as he and others were trying to serve a warrant as part of a Drug Enforcement Administration raid on a house.
The alleged shooter, Jarvis Hardy, has been indicted on eight counts, including attempted murder of a federal officer.