Adams, who is also eligible for the next Olympic cycle, is a direct replacement for Ben Sigmund who is carrying a niggling injury from the latter stages of the A-League season.
After captaining New Zealand in last year's World Cup qualifier against Mexico, Smith skipped the 4-2 loss to Japan in March to focus on his club career. Smith has played 4,1400 minutes of football over 46 games this season for Leicester and last week he told twtd.co.uk that 'the body has had a long season and needs a rest.'
"The people in New Zealand are happy with that," he said. "I think they understand the rigours, especially the interim coach, Neil Emblen. He has played in the league so he knows and he understands completely. As much as they'd like me to be there they can understand where I'm coming from."
Wood's recently promoted Leicester City have their final game of the season against Doncaster this weekend, and has chosen to 'rest' in his offseason, as he prepares for a Premier League preseason.
Reid has recently returned from an ankle injury which kept him out of action for the majority of this year and will also remain in England.
Elsewhere the squad is largely unchanged from the Tokyo trip as New Zealand Football continue to invest in players with qualification for the 2018 FIFA World Cup in mind.
With six teenagers named in the squad and another five aged 25 or under interim All Whites coach Neil Emblen is looking to build on the positive aspects taken from the defeat to Japan
"As a coach you're excited by the attacking options we have now and the speed of movement and passing that we showed at times last month against a very good side off to a World Cup," Emblen said.
All Whites squad - international v South Africa (Caps/Goals/Club)
Goalkeepers
Glen Moss (captain - 27/0, Wellington Phoenix)
Tamati Williams (0/0, Auckland City)
Defenders
Luke Adams (0/0, Unattached)
Michael Boxall (8/0, Wellington Phoenix)
Andrew Durante (7/0, Wellington Phoenix)
Storm Roux (2/0, Central Coast Mariners, AUS)
Bill Tuiloma (3/0, Olympique de Marseille, FRA)
Midfielders
Cameron Howieson (7/0, Burnley, ENG)
Chris James (17/2, unattached)
Michael McGlinchey (26/3, Vegalta Sendai, JPN)
Matt RidentoN (0/0, Wellington Phoenix)
Marco Rojas (17/1,Vfb Stuttgart, GER)
Tim Payne (9/2, Blackburn Rovers, ENG)
Ryan Thomas (1/0, PEC Zwolle, NED)
Forwards
Kosta Barbarouses (25/2, Melbourne Victory, AUS)
Tyler Boyd (1/0, Wellington Phoenix)
Jeremy Brockie (43/0, Wellington Phoenix)
Shane Smeltz (50/23, Perth Glory, AUS)