David Silva has been released from the Spain squad for personal reasons.
He started the 1-1 draw against the World Cup holders in Dusseldorf on Friday and was replaced by Real Madrid's Lucas Vasquez in the 71st minute.
Spain on Saturday announced via Twitter that Silva has left the national team camp, meaning he will not face beaten 2014 finalists Argentina at Atletico Madrid's Wanda Metropolitano on Tuesday.
Silva has also spent time away from the City this season and announced in January that his son Mateo has been receiving treatment after being born "extremely" prematurely.
He missed City's training camp in Abu Dhabi earlier this month so that he could spend time with his prematurely-born son.
City boss Pep Guardiola explained how Silva has been keeping himself fit during a difficult time in the influential player's personal life.
"He's just strong. We've said many times family is the most important thing," Guardiola told reporters.
"He wants to be here but sometimes he needs to go back and see his son – he's doing well – and his wife.
"But, of course, he knows he has to train. At the beginning it was okay but it's a long time without training – you cannot play good.
"He trains alone in Valencia when he goes there. When we go to Abu Dhabi he will stay here and in Spain because, again, family is the most important thing.
"Hopefully he can solve [the situation] as soon as possible, his lovely kid can grow and grow back at home and he can stay with us all days."
City return to action away to Everton in the Premier League on March 31.