The southern franchise produces five All Blacks in the 33-man squad.
Ben Smth, Waisake Naholo, Aaron Smith, LIam Squire and Lima Sopoaga are included, while Liam Coltman is injury cover for Dane Coles.
Fekitoa and Dixon, who were All Blacks last year, miss out.
Dixon, Ash Dixon, Rob Thompson, Joe Wheeler and Ton Franklin have been named in the NZ Maori side which play the Lions on June 17.
The bonus for the Highlanders is that Fekitoa will play the Lions next Tuesday. It has also been announced that Coltman, Sopoaga and Naholo will be free to play the Lions as they need to improve their match fitness.
Jordie, Beauden and Scott Barrett are the first sibling trio to be named in the same All Blacks squad and will be just the fourth set of three brothers to play for the All Blacks, following the Brownlie and Nicholls brothers in the 1920s and the Whitelocks in recent years.
All Blacks head coach Steve Hansen said: "Obviously, it's a very special occasion for the Barrett and Laumape families, with Jordie and Ngani being selected for the first time.
''Jordie has been in outstanding form, he has a skillset which is complete and has a great running and kicking game.
''Ngani too has been impressive throughout the Super season and has forced his way in through commanding performances," Hansen said.
Backs: Ben Smith, Israel Dagg, Jordie Barrett, Julian Savea, Waisake Naholo, Nganai Laumape, Rieko Ioane, Anton Lienert-Brown, Ryan Crotty, Sonny Bill Williams, Beauden Barrett, Aaron Cruden, Lima Sopoaga, Aaron Smith, TJ Perenara, Tawera Kerr-Barlow.
Forwards: Kieran Read (captain), Liam Squire, Sam Cane, Ardie Savea, Jerome Kaino, Sam Whitelock, Brodie Retallick, Luke Romano, Scott Barrett, Owen Franks, Charlie Faumuina, Ofa Tu'ungafasi, Wyatt Crockett, Joe Moody, Dane Coles, Codie Taylor, Nathan Harris.
Injury cover: Liam Coltman, Vaea Fifita, Jack Goodhue, Akira Ioane, Matt Todd.
- additional reporting NZME