Brazil appealed against Silva’s caution, but – as expected – they were not successful so former Chelsea man Luiz will take the armband in Tuesday’s semi-final.
FIFA's disciplinary committee refused to consider the appeal - appeals against yellow cards are only permitted in exceptional circumstances.
Thiago picked up the caution against Colombia, imposed after he blocked goalkeeper David Ospina taking a kick, and as it was his second of the tournament he was automatically suspended.
A FIFA statement said: "The disciplinary committee... cannot consider the matter given the fact that there is no legal basis entitling it to grant such request."
Luiz said: "I'm ready. I'm vice-captain and this group is very easy to handle because everyone's very down to earth. It won't be a tough job at all."
Luiz has the full support of Zenit St Petersburg striker Hulk, who insists the centre-back is the perfect man for the job.
"He's just the best," Hulk said. "He's very caring and very attentive, no matter who he's with. It's not every day that you come across someone like him.
"The whole world knows what he has to offer on the pitch - and to my mind, he and Thiago are the best central-defensive partnership in the world – but as his team-mates, we also know what a great person he is too."
Luiz is expecting a tough match against Germany, who are hoping to avoid a fourth successive World Cup semi-final defeat.
"They are a great team with a great philosophy of how to play football,” he said. "They have a lot of great players, a great coach and it will be a great game. It is a World Cup semi-final."
Thiago says he will "suffer" on Tuesday evening but remains confident they will rech the final.
"I was trying to avoid making fouls against Colombia. I think it was the only one I committed in the match, so it's difficult not being in this game and I'll suffer," the Paris St Germain defender said.
"It'll be tough but I don't think my mission is complete in this World Cup. It's made the group more united, the fact that Neymar and I can't play. It strengthens the group immensely."
Thiago says the man who will replace him against the Germans - Bayern Munich's Dante - is a fine replacement.
"He's ready. He works very hard. He is one of the first out at training and one of the last to leave, so he has the energy and the skills," he said.
"I played with him in 2004 and I know what he overcame to get here. This could be his moment to go out there and show his abilities."