The video, which was posted on Victoria Beckham's Twitter profile, showed the teenager kneeling on the grass and announcing who he will nominate, before being drenched in ice cold water by David and a friend.
He later runs off loudly complaining: "That's so cold! So cold!"
Victoria was nominated on Monday to complete the ALS Ice Bucket challenge by Eva Longoria but has yet to take part. However she teased fans by captioning Brooklyn's video: "Brooklyn's turn for the ! Getting prepared for my turn! X vb"
Former footballer turned underwear model David completed his challenge earlier in the day in the same gardens as Brooklyn.
He introduced the video by saying: "Hi, I'm David Beckham and I'm accepting Ryan [Seacrest's] ALS Ice Bucket challenge."
He later nominates sports stars Michael Jordan and Magic Johnson, and Hollywood star Leonardo DiCaprio.
The ice bucket challenge has taken social media by storm and some of the biggest celebrities have taken part, including Bill Gates and Justin Bieber.
The challenge aims to raise as much money as possible for the research and treatment of motor neurone disease and involves filling a bucket with ice cold , and then pouring it over yourself, all while being videoed as hilarious proof for friends and social media followers. The drenched participant must then nominate three more people to experience the gruelling ice shower.