Speaking during his usual 8pm slot on Thursday evening, Mr Neil said he would be away for a “few weeks” but would be back “before summer is out”.
Former Sky News presenter Colin Brazier will cover his show while he is away.
Mr Neil also acknowledged that the channel had experienced a “rocky start” but said GB News’ audience was growing.
“In two short weeks, we’ve already built a loyal audience which has beaten all of our expectations, it’s often bigger than the other news channels and it’s growing,” he said.
“That’s the real story about GB News to date and you won’t often read that in the papers.
“So on behalf of GB News, I say to all of our viewers, thank you. We won’t let you down and you ain’t seen nothing yet.”
Swedish furniture giant Ikea said it had “not knowingly” advertised on the channel.
A spokesperson said: “We are in the process of investigating how this may have occurred to ensure it won’t happen again in future, and have suspended paid display advertising in the meantime.”
In its statement, Kopparberg also said it was unaware its adverts were running on the channel and said they had been suspended “pending further review of its content”.
But Octopus said it would only advertise with GB News if it proved to be “genuinely balanced”.
The Open University has also paused its advertising.
GB News has vowed to fight cancel culture and reflect voices not heard in the media but has faced criticism from campaign groups such as Stop Funding Hate.
Critics have compared it to the highly partisan Fox News but Mr Neil, who is the BBC’s former political editor, has dismissed comparisons to Fox as “nonsense”.
Mr Neil has said GB News will challenge the “echo chamber” of the “metropolitan” news.