Back-row forwards Alasdair Strokosch and Kelly Brown will miss the rest of Scotland's summer tour after being injured in the win over Canada.
Perpignan flanker Strokosch, 31, was stretchered off with a neck injury and Saracens' Brown, 32, was also replaced.
Both were due to be rested for the final two Tests of the tour.
However, Vern Cotter's coaching team had considered keeping them with the squad for Friday's game in Argentina before injuries ruled them out.
London Irish duo Blair Cowan and Kieran Low, who were due to return home, will now travel on to Buenos Aires with 11 others for the South American leg of the tour.
Another group of players set off from the UK on Saturday to join up with the squad for the Test meetings with the Pumas and South Africa, with the final match on 28 June.
Gloucester half-back Greig Laidlaw, who captained the side in Houston and Toronto, and Newcastle prop Scott Lawson are among those leaving the tour at the midway stage.
Scotland team doctor James Robson says flanker Strokosch "will require a short period of recovery for soft-tissue injuries" while Brown has suffered damage to his left arm.
Scotland squad v Argentina
Forwards: Kevin Bryce (Glasgow Warriors), Blair Cowan, Geoff Cross (both London Irish), David Denton, Alasdair Dickinson, Ross Ford (all Edinburgh), Chris Fusaro (Glasgow Warriors), Grant Gilchrist (Edinburgh), Jonny Gray, Rob Harley (both Glasgow Warriors), Kieran Low (London Irish) Moray Low (Exeter Chiefs), Pat MacArthur, Gordon Reid (both Glasgow Warriors), Tim Swinson, Jon Welsh (both Glasgow Warriors).
Backs: Alex Dunbar (Glasgow Warriors), Dougie Fife, Grayson Hart (both Edinburgh); Stuart Hogg, Peter Horne (both Glasgow Warriors), Ruaridh Jackson (London Wasps), Sean Maitland, Peter Murchie, Henry Pyrgos, Tommy Seymour, Duncan Weir (all Glasgow Warriors).