Conspiracy theorist Mr Jones had already been permanently banned from the social media site after numerous warnings about violations of Twitter’s terms and conditions.
On Twitter and elsewhere, Mr Jones had described survivors of a shooting at a school in Parkland, Florida, as "crisis actors" and said the mass killing at Sandy Hook Elementary School in 2012 was fake.
He had approximately 900,000 followers on Twitter and Infowars had around 430,000.
The social media site said Mr Jones would not be able to create new accounts or take over existing ones.
At the time, Twitter said it would monitor reports about other accounts potentially associated with Mr Jones or Infowars, and would “take action” if it finds any attempts to circumvent the ban.
Other tech companies, including PayPal, YouTube, Apple and Spotify, have limited or banned Mr Jones' activities on their sites.
Infowars said the moves are intended to sabotaging the site just weeks before the midterm elections.
A Twitter spokesman confirmed that the accounts had been removed but provided no additional comment. The company said it usually does not discuss specific accounts.