The social networking platform - which has faced increasing pressure to block Jones - has not revealed what prompted the decision and has opted to still make his old tweets viewable to other users while his account remains locked in a "read-only" mode.
According to the New York Times newspaper, the decision was taken after Jones posted a link to a video in which he called on his followers to prepare their "battle rifles".
Speaking to NBC, Twitter chief executive Jack Dorsey explained that Jones had been put on a "timeout" by the platform.
In response to accusations that the move was too lenient, he added: "Well, I feel, you know, any suspension, whether it be a permanent one or a temporary one, makes someone think about their actions and their behaviours."
By contrast, Dorsey previously said Jones will not be banned by Twitter because his accounts did not violate the website's rules.
Speaking earlier this month, he wrote: "We didn't suspend Alex Jones or Infowars yesterday. We know that's hard for many but the reason is simple: he hasn't violated our rules. We'll enforce if he does. And we'll continue to promote a healthy conversational environment by ensuring tweets aren't artificially amplified. (sic)"