The 27-year-old scored five goals against Newcastle last weekend but was then withdrawn in the second half. admitting he had felt his hamstring in City's previous game against Borussia Monchengladbach.
However, Argentina boss Gerardo Martino claimed his latest problem was unrelated.
Aguero was stretchered off during the first half of Argentina's 2-0 defeat to Ecuador on Thursday.
"The studies we did today show that Sergio Aguero has a grade-two muscle tear in the left hamstring," the Argentine Football Association said in a statement on Friday.
Argentina ruled Aguero out of next week's World Cup qualifier against Paraguay but did not speculate how long he would be sidelined for.
However, a grade-two tear to the hamstring can require anything from two to eight weeks to recover from and the striker has a history of hamstring problems.
The injury is expected to see Aguero miss the Manchester derby on October 25 and Champions League matches with Sevilla on October 21 and November 3.
Silva added to City's worries when he was forced off after just 11 minutes of Spain's clash with Luxembourg on Friday, a match which also saw Juventus star Alvaro Morata stretchered off.
Spain boss Vicente Del Bosque said after the game: "I do not know the extent of the injuries.
"Our doctors will inform you when they know something. We know nothing for now."
Spain won 4-0 to secure their spot in the Euro 2016 finals.