City expect the striker to be out until mid-September after suffering a knee injury in last week's opening Barclays Premier League win over Southampton. But that has not stopped Argentina coach Alejandro Sabella naming the 24-year-old in his squad for World Cup qualifiers against Paraguay and Peru on September 7 and 11 respectively.
Mancini said: "It is impossible because Sergio needs a minimum of two weeks without training. After two weeks he can start again. If in one week if he could be ready to play it is different, but I think he needs another two weeks. He can go and fly back quickly. These are the rules and we need to respect them - they are ridiculous rules."
City had initially feared a longer lay-off for their £38million club record signing, who scored 30 goals last season.
Aguero was carried off after falling awkwardly following a fair tackle from Nathaniel Clyne early in City's 3-2 win over Southampton at the Etihad Stadium.
Mancini said: "Maybe after the international break he will be ready - three or four weeks.
"It's a bad knee injury but not for six months - two or three weeks.
"After two weeks he can start to train maybe and in four weeks he can play, maybe.
"We are lucky with Sergio because he can be very strong after injuries."
Source: PA
Source: PA