Strokosch left the field on a stretcher following a blow to his shoulder/neck but after a precautionary visit to hospital returned to the team hotel.
"He will require a short period of recovery for soft-tissue injuries," explained Scotland team doctor James Robson.
Brown suffered damage to his left arm/shoulder and will return home to the care of his club medical team. Although both had been scheduled to leave the tour at this juncture, management were assessing whether they would travel to Argentina before yesterday's events ruled out that scenario.
The London Irish back-row duo, Kieran Low and Blair Cowan, and their new club colleague at prop, Geoff Cross, all substitutes yesterday, will travel on with Gordon Reid, Pat MacArthur, Kevin Bryce, Moray Low, Grant Gilchrist, Tim Swinson, Grayson Hart, Peter Horne, Sean Maitland and Stuart Hogg to Argentina.
The home-based players who set out from the UK yesterday have arrived in Buenos Aires and will begin preparations with their team-mates when they arrive from North America tomorrow. The third match of Scotland's tour is against the Pumas in Cordoba on Friday.