Sharif was at the Doha Tribeca Film Festival for a screening of one of his movies ... when a woman approached him on the red carpet ... and tried to take a picture with the 79-year-old actor.
Sharif -- who was nominated for an Oscar in 1962 for his role in "Lawrence of Arabia" -- lashed out in Arabic ... telling the woman to wait her turn ... and then slapping her.
Moments later, the woman smiled and posed for a photo with Sharif like nothing ever happened.
Watching from the video, it's unclear if Sharif made contact with the woman's face -- but one reporter who was at the scene tweeted, "Omar Sharif just hit a woman. Very stupidly, in front of a camera."
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