But Dylan Hartley and Courtney Lawes have been retained as part of a 26-man squad preparing for the clash with the Pumas.
Francis, who moved to Northampton from Super Rugby side the Blues during the summer, was one of the 33 players called up on Sunday, but he has now been allowed to return to Franklin's Gardens.
Saracens duo Owen Farrell and Alex Lozowski are joined by Leicester's George Ford in the battle for the No.10 shirt.
But Hartley and Lawes look set to play key roles against Argentina, with the former likely to captain his country, as he has done so well in recent times.
Backs: Mike Brown (Harlequins), Elliot Daly (Wasps), Jonny May (Leicester Tigers), Semesa Rokoduguni (Bath Rugby), Anthony Watson (Bath Rugby), Danny Care (Harlequins), Owen Farrell (Saracens), George Ford (Leicester Tigers), Jonathan Joseph (Bath Rugby), Alex Lozowski (Saracens), Henry Slade (Exeter Chiefs), Ben Youngs (Leicester Tigers)
Forwards: Tom Curry (Sale Sharks), Nathan Hughes (Wasps), Maro Itoje (Saracens), George Kruis (Saracens), Joe Launchbury (Wasps), Courtney Lawes (Northampton Saints), Chris Robshaw (Harlequins), Sam Underhill (Bath Rugby), Dan Cole (Leicester Tigers), Ellis Genge (Leicester Tigers), Jamie George (Saracens), Dylan Hartley (Northampton Saints), Mako Vunipola (Saracens), Harry Williams (Exeter Chiefs)