Milner-Skudder, the 2015 World Rugby Breakthrough Player of the Year, missed much of last season when he suffered a shoulder injury that required surgery.
In January, the All Blacks winger extended his contract with the Hurricanes and New Zealand Rugby until after the 2019 World Cup in Japan.
The 26-year-old made some limited appearances in the Hurricanes' pre-season games but coach Chris Boyd said he had been struggling with a hamstring injury and the decision had been made to leave him in Wellington.
Injured prop Loni Uhila (calf) was also omitted from the squad travelling to Tokyo.
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"If we had been playing at home they may have been considered, but to sit on a long haul flight with a muscle injury like that was probably not a great idea," Boyd said before the team left for Japan.
"It's a long season, so we decided the prudent move was to leave them at home and get them 100 percent right for our first home game against the Rebels in two weeks time," added Boyd.
Milner-Skudder's absence is likely to give new recruit Jordie Barrett an opportunity to start at fullback.
The younger brother of World Player of the Year Beauden, Barrett moved north from the Canterbury provincial side to play with his flyhalf brother at the Hurricanes.
He was taken on the All Blacks' European tour last year as an "apprentice" to introduce him to the team culture and give the coaches a chance to work with him, but was not considered an official part of the squad.
Boyd's travelling 25-man squad includes five players who turned out for the All Blacks last year in TJ Perenara, captain Dane Coles, Julia and Ardie Savea and Beauden Barrett.
Last year's champions face the Sunwolves on Saturday, while their opponents next week, the Melbourne Rebels, open the 2017 competition against the Auckland Blues on Thursday.
(Reporting by Greg Stutchbury; Editing by Peter Rutherford)
