The 23-year-old missed City's win over Aston Villa last month after suffering a similar injury in the first half of the 4-0 win at Blackburn.
The Albiceleste face Bolivia later today in Buenos Aires, with Paris St Germain's Javier Pastore standing by to take Aguero's place if the City man does not make it.
Technical director Alejandro Sabella told the Argentinian Football Association's website: "Sergio Aguero has a sore groin and is doubtful for the match against Bolivia. In the event that Aguero does not play, Javier Pastore may replace him.
"The rest of the team to play Bolivia is: Sergio Romero, Pablo Zabaleta, Nicolas Burdisso, Martin Demichelis, Clemente Rodriguez, Fernando Gago, Javier Mascherano, Ricardo Alvarez, Lionel Messi and Gonzalo Higuain. We do not know whether Aguero will be able to play."
The game against Colombia follows on Tuesday in Barranquilla.