TrueTube, an educational platform, has been named a contender for three awards in total, including best drama and secondary learning.
Horrible Histories also earned three nominations, all for its special episode celebrating the 400th anniversary of Shakespeare's death.
The awards will be held at the Roundhouse in London on 20 November.
TrueTube's success "demonstrates the shift in how young audiences are consuming media", Bafta said.
The website's drama nomination is for Refugee, a 12-minute film following a British girl and her family who have fled their home, while Katie, about a gay, Catholic nurse in a children's ward, is up for the learning award.
TrueTube senior education producer Bob Ayres said: "We are over the moon. We are a small charity-funded online channel and to be nominated alongside such giants feels like an attack of vertigo.
"We are very, very proud the films we make for young people and schools have been given such recognition, and extremely pleased they will now reach a wider audience."
The Shakespeare special from the gruesomely entertaining Horrible Histories is up for the comedy and writing trophies and actor Tom Stourton will compete for the best performer honour for playing the role of the Bard.
Elsewhere, a number of programmes received two nominations. Cartoon Network's The Amazing World of Gumball is up for the animation and writer awards.
CBBC's Hetty Feather and The Dog Ate my Homework are among the other double nominees.
The annual Bafta Children's Awards also recognise movies which have been on general release in UK cinemas.  This year, the academy has chosen Zootropolis, The Good Dinosaur, The Jungle Book and Star Wars: The Force Awakens for its feature film award.
Star Wars is also in the running for two other awards - best game for Lego Star Wars: The Force Awakens and the adapted interactive prize for Star Wars Arcade.
The full list of categories and nominees can be found on the Bafta website, with voting closing on 18 November.
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The Bafta Children's Awards have for the first time nominated an online-only service for channel of the year.