The clash with the Pumas will be the 27-year-old's first-ever Test start out wide but he impressed in that position after replacing Cueto in the early stages of last month's win over Ireland.
"It's quite a simple decision. Delon has been around for a few years now - we know when he is in form he is a Test match player," said England team manager and former Lions hero Martin Johnson.
"We've no qualms about picking him in any of the back three positions."
Cueto was forced out of the 20-9 success in Dublin after just 21 minutes and has been having pain-killing injections ever since.
England hope the Sale star will be available for selection for the second pool game against Georgia on September 18 but he joins skipper Lewis Moody in missing the Pool B opener.
"Mark's had a little bit (of back trouble) before but he could have played," added 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. The good things for us is Delon is playing very well."
Nick Easter returns to the side at No8 in the only other change to the side that finished their World Cup warm-up series with a win.
The Harlequins veteran replaces tournament absentee Hendre Fourie in the back row, with James Haskell switching to the openside flank.
Jonny Wilkinson is preferred to Toby Flood at fly-half, while Richard Wigglesworth will be his halfback partner after a fit-again Ben Youngs was only named on the bench.
"Jonny's in good form and we know what he brings to the table. It's a good decision to have to make. Jonny just got his nose in front for this game, although that may change for this week or the week after, whatever we think is best.
"Jonny's been in great form, as has Toby, and it's a great place to be to have two 10s step up and start for us.
"Wiggers is a savvy player, he's been around a little bit longer than the other two [scrum-halves] and he's taken the responsibility well. He's got a real maturity about him and it gives us some real experience."
England (vs Argentina, Dunedin, Saturday, 9.30am BST)
Ben Foden; Chris Ashton, Manu Tuilagi, Mike Tindall (captain), Delon Armitage, Jonny Wilkinson, Richard Wigglesworth; Andrew Sheridan, Steve Thompson, Dan Cole, Louis Deacon, Courtney Lawes, Tom Croft, James Haskell, Nick Easter
Replacements: Dylan Hartley, Matt Stevens, Tom Palmer, Tom Wood, Ben Youngs, Toby Flood, Matt Banahan
NB bold denotes Lion