The pair are big doubts for their country's final warm-up game, against Slovenia on Saturday, and now face a battle to be fit in time for the World Cup
Manchester City striker Aguero and defender Garay were both unused substitutes as Argentina's preparations for the tournament continued on Wednesday with a 3-0 win over Trinidad and Tobago.
And the Argentinian Football Association (AFA) have now confirmed that the pair face fitness battles, with the start of the World Cup looming large on the horizon.
Aguero has endured an injury-hit 2013-14 at club level and started just 20 of his side's 38 Premier League games en route to being crowned champions of England.
When fit, though, Aguero's influence was clear, as he scored 17 league goals and netted 28 times in total in competitions.
Like Aguero, Garay also heads to Brazil having won a domestic title - with Benfica in the Primeira Liga.
Question marks now remain over of what part - if any - Aguero and Garay will play in Saturday's final friendly with Slovenia.
Argentina's World Cup campaign begins against Bosnia-Herzegovina on June 15.