Paparazzi gathered outside the entrance to Craig's restaurant in West Hollywood aiming to grab a picture of the power couple on Monday, October 15 - and stood in front of their Cadillac Escalade sports utility vehicle as it left the venue.
Footage obtained by TMZ.com shows their driver pulling out of the eatery's car park slowly and carefully, but knocking down a snapper who failed to get out of the way as their car passed through a gate.
The photographer was floored by the accident, prompting witnesses to yell out to the couple's driver, who briefly stopped without getting out of the vehicle to check if the victim was seriously harmed by the accident.
Although some fellow photographers remonstrated with Jennifer and Alex's chauffeur, he blamed the incident on their flashbulbs, saying, "See what happens when you flash all the flashes? I can't see where I'm going."
The "Waiting for Tonight" singer, 49, and the retired baseball star, 43, have become regulars at the all-American restaurant since they began dating last February (17). The restaurant is also favoured by stars including Kim Kardashian and George Clooney.
As the fallen photographer got to his feet, the accident looks less serious than an incident last year - when Justin Bieber knocked over another paparazzo while leaving his church in a pick-up truck.
Snapper Maurice Lamont was taken to hospital after the accident but absolved Justin of blame in a video posted on Instagram from his hospital bed.
"He got out, he was compassionate, he was a good kid," Maurice said of the "Sorry" singer. "Accidents happen."