The company announced this morning that accounts thought to be used by Mr Jones to circumvent a previous ban have been taken down.
It follows an earlier ban on the alternative media commentator, known for his aggressive tirades on the air, and publicity of conspiracy theorists, which he calls his "fight for freedom of speech".
A spokesman confirmed that the accounts had been removed but wouldn't reveal any specific Twitter handles.
The @realalexjones and @infowars accounts were permanently banned from both Twitter and Periscope in early September, based on "reports of tweets and videos that violated its policy against abusive behaviour," a company spokesman said.
Mr Jones reportedly attended a Donald Trump rally in Houston on Monday, and was filmed outside the venue screaming at a pile of excrement on the road.
When Alex Jones’ security detail signed up for this gig, do you think they ever imagined standing watch while their protectee filmed himself screaming at a pile of excrement? 🤷♂️ pic.twitter.com/S1R33hIdPC— Josh Campbell (@joshscampbell) 23 October 2018
He was also seen ranting at liberal protesters who had brought along the balloon of Mr Trump depicted as a baby.
On Twitter and elsewhere, Jones has done such things as describe survivors of a shooting in Parkland, Florida, "crisis actors" and saying the mass killing at Sandy Hook Elementary in 2012 was fake. He had about 900,000 followers on Twitter. InfoWars had about 430,000.
InfoWars claimed the move was meant to sabotage the site just weeks before the US midterm elections.
It said on its website: "Infowars is under unprecedented attack and is being censored across the internet. Our podcasts have been removed from iTunes, Spotify, Stitcher and other platforms – along with YouTube banning The Alex Jones Channel."
Twitter said it would continue to evaluate reports regarding other accounts potentially associated with InfoWars and would take action if it finds content that violates its rules, or if other accounts are used to try to circumvent their ban.
Other tech companies, including PayPal, YouTube, Apple and Spotify, have also limited or banned Mr Jones's activities on their sites.