Beckham, 39, had been at the training London training ground, watching his eldest son Brooklyn, 15, play for the club’s under-16 side against Brighton.
Thomas Cadman, who played for Brighton under-16s against Brooklyn's side, said on Twitter: "Weird to play against Brooklyn Beckham earlier. Even weirder to be currently stuck behind David Beckham as he has crashed his car."
Archie Davies, a team-mate, said: "Just seen David Beckham looks like he got in a car crash and hurt his shoulder. Star struck by seeing David Beckham tbh."
It's been claimed that the incident involved one other vehicle and although David appeared to injure his shoulder in the collision, he is not thought to be hurt badly.
Brooklyn, 15, was signed by Arsenal on a short-term contract earlier this month, while his brothers - Romeo, 12, and Cruz, nine - have also been playing for the club's youth teams.
Before joining Arsenal, Brooklyn was linked to other football clubs in the English Premier League, including Chelsea.