The 24-year-old has been named in the national squad for their two matches against Paraguay and Peru on September 7 and 11, despite being stretchered off with a knee injury in the Citizens’ 3-2 win over Reading last Sunday.
Scans have revealed the injury is not as serious as first feared but the diminutive striker is still likely to be out of action for a month, prompting a confused reaction from Mancini over the international call-up
"I don't understand this, I don't understand," Mancini told BBC Sport.
"The national manager should understand this is a serious case. A bad injury."
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According to reports, City and Argentina officials are due to meet within the next 24 hours as the Premier League champions aim to keep their star striker from travelling.
Mancini also expressed concern at staging international matches so early into the domestic season.
"These games are really strange because all the players are not ready to go. I don't understand this. Sometimes the players are not ready for this game," he added.
"Aguero is not so bad like we thought. After the international break he will be ready. Two or three weeks. It is a bad injury but not for six months. After two weeks he can start to train maybe."