Labbadia was dismissed after starting the new Bundesliga campaign with three successive defeats, the latest of which came in a 2-1 loss at Augsburg yesterday.
Stuttgart have decided to appoint from within to find a swift replacement, with Schneider promoted from coaching the under-17's to the senior side.
Schneider has signed a two-year deal at the Mercedes-Benz Arena, and the 40-year-old said he is relishing the chance to make a successful step up.
He told reporters at a press conference this afternoon: "I am really looking forward to the job in hand and am full of confidence."
Schneider's first priority is to overturn a 2-1 deficit to Croatian side Rijeka in the Europa League, with the second leg to come on Thursday in his debut as boss.