In a social media post earlier this week Ngata-Aerengamate alleged Moore told her she didn't deserve to be in the team and she was selected only to play the guitar.
The end of year Northern Hemisphere tour was a tough one for the Black Ferns.
They lost all four tests, beaten convincingly by England and France in what was their first international rugby in two years due to Covid.
New Zealand Rugby chief executive Mark Robinson says the independent inquiry will run alongside the review the NZR is doing of the Black Ferns end of year tour.
Robinson said the terms of reference are being drawn up and a panel including rugby and non-rugby people being sought.
"We have a huge amount of sympathy for anyone going through a challenging time like this...I know that our people have been in contact with Te Kura to make sure that she has got all the support possible at this time.
Robinson said they also wanted to "understand" what Ngata-Aerengamate wanted to see as part of the review.
Robinson wouldn't give his thoughts on the tenor of the alleged comments.