The 7-2 second favourite will also miss the remainder of the season.
Mullins tweeted: "It looks like he has a little chip off a sesamoid bone which will need to be removed."
The six-year-old's withdrawal comes a week after 2015 winner and stablemate Faugheen was also ruled out of the race on 15 March.
Faugheen and Arctic Fire's injuries mean another Mullins runner, Annie Power, may now be added to the Champion Hurdle field for a supplementary fee.
Mullins, who trained all of last year's top three finishers, also has Nichols Canyon entered for this year's race.
Last year's Champion Hurdle runner-up Arctic Fire will miss next month's race at the Cheltenham Festival through injury, says trainer Willie Mullins.