The five-minute episode, called "Spider's Web", features an apparently innocuous spider called Mr Skinnylegs.
The family takes a great interest in the spider and learns to avoid disturbing its web.
But a viewer in Australia, which has some of the world's most venomous spiders, complained in 2012 about the episode's message that the insects "are not scary".
The ABC agreed that the episode sent the wrong message to children and apologised for running it.
In the banned episode, Daddy Pig is seen repeatedly picking up the spider by a string from its web.
The family learns not to disturb Mr Skinnylegs' web after Daddy Pig declares: "It's hard work weaving a web ...
No deaths from funnel web spiders have been recorded since an antivenom was introduced in 1981. »