Cueto has been struggling with a lower back problem since the week of England's final warm-up international against Ireland, when he was forced off just 21 minutes into the game.
London Irish full-back Delon Armitage will make his first Test start on the wing while Nick Easter returns at number eight after missing the Aviva Stadium victory with a tight calf.
Mike Tindall captains the team again from inside centre with Manu Tuilagi, one of 10 World Cup debutants in the team, to make his third Test appearance at outside centre.
With Easter back at number eight and squad captain Lewis Moody still sidelined with a knee injury, James Haskell returns to start at openside flanker.
Saracens' Richard Wigglesworth continues at scrum-half but Ben Youngs, who missed England's three warm-up games after undergoing a knee operation, has been included on the bench.
Johnson insisted Cueto could have played in an emergency but Armitage's form, which brought him a try off the bench in Dublin, meant England had a simple decision to make.
"Mark's had a little bit (of back trouble) before but he could have played (against Argentina)," said Johnson.
"There's a grey area between fit and injured in where most players sit all of the time.
"He trained fully all week but he's not quite where he needs to be - but the good things for us is Delon is playing very well.
"It's quite a simple decision. Delon been around for a few years now, we know when he is in form he is a Test match player. We've no qualms about picking him in any of the back three positions."
Argentina named their team on Tuesday, making just one change from their warm-up defeat to Wales with former Harlequins and London Irish centre Gonzalo Tiesi returning to the midfield.
"They do what they do very well but they've got more dimensions to them than is sometimes made out," said Johnson.
"They are a dangerous running side, they come at you through forwards but put you under pressure with their kicks as well. It's a full-on Test against a team that finished third in the world last time.
"You have to get it right in the moment, right from the opening kick-off."
England team to play Argentina in the Rugby World Cup at Otago Stadium, Dunedin on Saturday, September 10 (kick-off 9,30am BST):
B Foden (Northampton); C Ashton (Northampton), M Tuilagi (Leicester), M Tindall (Gloucester, capt), D Armitage (London Irish); J Wilkinson (Toulon), R Wigglesworth (Saracens); A Sheridan (Sale Sharks), S Thompson (London Wasps) D Cole (Leicester), L Deacon (Leicester), C Lawes (Northampton), T Croft (Leicester), J Haskell (Ricoh Black Rams), N Easter (Harlequins).
Replacements: D Hartley (Northampton), M Stevens (Saracens), T Palmer (Stade Francais), T Wood (Northampton), B Youngs (Leicester), T Flood (Leicester), M Banahan (Bath).
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