Both Barrett and Fifita suffered their concussions in last night's 26-13 win over France in Wellington.
Barrett's incident occurred in the 12th minute of the match when he collided in mid air with France fullback Ben Fall.
Fall was red carded for the incident because Barrett landed on his neck and head.
Coach Steve Hansen says both Barrett and Fifita will stay in Wellington tonight and will be monitored throughout the week.
Hansen said a decision will be made later in the week on whether they'll join the group in Dunedin ahead of Saturday's test.
