A statement from Rugby World Cup organisers confirmed that the case will be heard by the independent judicial officer Bruce Squire QC from New Zealand. The hearing will take place in Auckland at 4pm local time.
The incident involving the players occurred at a ruck during the first half of the game. Healy was left wincing and immediately sought out referee Jonathan Kaplan to make an allegation of eye gouging.
Speaking on Monday, Ireland team manager Paul McNaughton told a press conference in Wellington that Healy had been interviewed to give his side of the story.
"We were asked questions and asked to make a brief statement on it to the match commissioner. We did that in the ground (after the game)," explained McNaughton.
"Cian answered several questions put to him by the match commissioner and gave a statement, but we haven't heard anything since."
Follow the Ireland team in New Zealand on www.twitter.com/irfurugby.