Quinn Roux, Will Addison, Stuart McCloskey and Darren Sweetnam are among the notable names absent from the squad.
Roux was involved in all of Ireland's Six Nations games, while McCloskey was named in the Pro 14 team of the season.
Munster's South African-born lock Jean Kleyn does make the 44-man panel, despite not being eligible until August.
Uncapped Munster full-back Mike Haley also gets the nod, with Sean O'Brien and Dan Leavy confirmed absentees through injury.
Schmidt will trim the squad to 31-players before flying out to Japan in September and says the door hasn't closed on players who have missed out so far.