Gabriel, 8, died from injuries sustained in the accident that also killed his father, 45, and his younger brother Byron, 5.
Dickson’s wife, Dusty, was injured in the crash.
A statement released by the AFL said: "The families of Robert and Dusty Dickson regretfully and with great sadness wish to inform relatives and friends that their beautiful boy Gabriel passed away peacefully, surrounded by family on Tuesday, April 14.
“A memorial service for Rob, Gabriel and Byron will be held at a future time back in Melbourne. Dusty and her family are thankful for your support, thoughts, prayers and love through this horrific time.”
Dickson, 45, played 17 matches for the Hawks from 1988-90 and two for the Brisbane Bears in 1991.
He was an emergency for Hawthorn in the 1989 grand final.
His most recent documentary, The Essence of the Game, was telecast on the eve of the AFL season.
Dickson also produced and directed The Passion to Play in 2001 and Shane Crawford Exposed in 2004.
Last week, AFL CEO Andrew Demetriou said staff at the AFL were devastated by Dickson's death.
"Rob was a personal friend and a great and positive force in life," Demetriou said.
"He was a wonderful filmmaker but above all he was a wonderful person who brought enormous empathy to what he was doing, whether it was filming a NAB Auskick clinic or Sam Mitchell standing in the middle of the MCG savouring a premiership medal.
"He was a friend to so many of us at the AFL and in the wider football world.
"I don't think there is one person at any level of the game who has met him who was not the better for being in his company because he was so passionate about life and our game.
"He was one of those rare people who could capture on film the passion and beauty of the game and to articulate in images exactly what we all love about the game but struggle to be able to put into words."
