Cardiff Blues scrum-half Williams suffered an ankle injury in training last week and is ruled out of the remainder of the tour.
He will return home to the UK on Sunday along with prop Paul James who has failed to recover from a calf injury.
Wales play the All Blacks on Saturday at Eden Park, the first of three Tests against the world champions in June.
Tight-head Aaron Jarvis arrived as injury cover for James on Wednesday.
Scarlets' uncapped scrum-half Aled Davies has arrived in New Zealand as an injury replacement for Lloyd Williams.