This is the first time a blanket ban has been imposed on Jones, who is now being sued by parents of children murdered in the 2012 Sandy Hook shooting for claims that the attack was a hoax.
Neither Jones nor a representative for Infowars were available for comment early on Monday.
"Apple does not tolerate hate speech, and we have clear guidelines that creators and developers must follow to ensure we provide a safe environment for all of our users", an Apple spokesperson said.
"While much of the discussion around InfoWars has been related to false news. none of the violations that spurred today's removals were related to this", it said in a statement. The company removed the Alex Jones Show along with five other podcasts produced by the organization, its entire lineup except for Real News with David Knight which remains active in the Apple podcast directory.
The development comes after Apple removed Jones' daily podcasts from its podcast directory. Last week, Facebook removed four videos on four of Jones' pages for violating its hate speech and bullying policies, according to a statement put out by the media platform.
The theories he has promoted include that the September 11, 2001 attacks on NY and Washington were staged by the USA government. Last week, YouTube removed four videos posted by Jones and issued a warning that more violations could result in a ban from the video platform.
It no longer links to series such as The Alex Jones Podcast and War Room in its apps.
Among other claims, he has called the 2012 Sandy Hook Elementary School mass shooting a hoax. The parents of two children shot in that attack are suing him for defamation, saying he had made "false, cruel, and risky assertions".
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He now admits the shooting occurred but says his claims were free speech. It also banned Jones' profile from posting to the social network for 30 days.
While running for president in 2015, Donald Trump told Jones his reputation was 'amazing'.
Also, Spotify, a music and podcast streaming company, said on Monday that it had now removed all of Jones's Infowars programs from its platform. Spotify took down several episodes of the show last week.
The move by Facebook is the latest crackdown on Jones, who has recently had content removed from other platforms.
Founded in 1999 and often described as "actually only a tiny bit worse than Fox News", InfoWars has over the years gained a large following among far right conservatives.
'I know countless writers and artists who use the service.
'And you're now hosting his podcasts??'