Little, which coincidentally came out just two months ago (April 2019), was executive-produced by co-star Marsai Martin, who was 14 at the time of its release and just 13 when it went into production. Wikipedia, citing this Grapevine article, describes her as "the youngest executive producer in Hollywood history".
The same article cites Millie Bobby Brown as being executive producer for a film adaptation of the Enola Holmes Mysteries books, in which she will also star. Brown was 13 when the adaptation was announced, but she's now 15 and it's still in production, so I'd say Marsai Martin still holds the title.
There is still the possibility that someone younger than 14 produced a TV series, but to be honest, I find it highly remote.