Mr Jones is currently banned from YouTube for violating the site’s policy on abusive behaviour.
He is also banned from many other social platforms for breaking conditions governing such behaviour.
The Hope Not Hate campaign said it was a mistake for Mr Paul to “give a platform to an extremist”.
A two-hour chat with Mr Jones features on the Logan Paul podcast channel, which currently has about 1.4 million subscribers, many of whom are in their teens and 20s.
During the wide-ranging interview Mr Paul laughs and jokes with Mr Jones about his widely contested beliefs, at one point going along with Mr Jones’s claim that former US presidential candidate Hillary Clinton is “crazy”.
However, Mr Paul does challenge Mr Jones, who is being sued for defamation by parents of children killed during the 2012 Sandy Hook school shooting, on his views on the massacre, saying his view of it as a hoax could “become something dangerous”.
Joe Mulhall, senior researcher at Hope Not Hate, criticised the decision to record and air the talk.
“Paul seems to have given a platform to an extremist simply to generate more views and appears to have portrayed his guest as an amusement,” he said.
He added: “Paul described Jones as “a far-right conspiracy theorist” and yet still decided to have him on his show, meaning he knew what he was doing and seemingly didn’t seem to care.”
Mr Mulhall said the show could mean Mr Jones is exposed to a “new and younger audience”.
Social platform ban
The interview looks set to get significant views as Mr Paul has more than four million followers on Twitter, where the chat was previewed.
And almost 19 million people subscribe to Mr Paul’s main YouTube channel.
Mr Paul and YouTube have yet to respond to requests for comment about the interview.
Many other social platforms have taken action against Mr Jones and his InfoWars media group.
Twitter has permanently banned Mr Jones and his InfoWars channel for repeatedly violating its terms and conditions.
Other bans have been imposed by Facebook, Apple, Pinterest and LinkedIn.
Paypal has also refused to process payments on behalf of InfoWars.