The five-minute episode, Spider's Web, features an apparently innocuous spider called Mr Skinnylegs.
The family take a great interest in the spider and learn 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 public broadcaster agreed the episode sent the wrong message to children and apologised for running it.
"The ABC considered the episode unsuitable for broadcast in Australia and it had been restricted from being aired on the ABC's television networks," the broadcaster said in a response in August 2012.
The complaint was reported in recent days by the local media, though it was not clear why the incident only emerged this week.
In the banned episode, Daddy Pig is seen repeatedly picking up the spider by a string from its web. "Don't be scared, Mummy," says Peppa.
Deaths from spiders are exceedingly rare in Australia and the creatures are less life-threatening than sharks or bees. Antivenom for most of the more dangerous spiders has been available for decades.
But this summer Australia has reportedly seen an increase in spider-related injuries that has led to public warnings.
Last year, Sydney paramedics attended 319 spider-related incidents. There have already been 102 incidents recorded this year.
No deaths from funnel web spiders, the most dangerous in the country, have been recorded since an antivenom was introduced in 1981.