Bundesliga coaching newcomer Schneider, a former Stuttgart player who managed the club's Under-17 team, signed a two-year deal.
"I was contacted last night and it was understood that I would help the team," the 40-year-old told reporters. "It is of course a difficult task in a brutal situation."
Labbadia, who joined Stuttgart in late 2010 and saw his team lose 2-1 to Augsburg on Saturday, becomes the first coaching casualty of the season after only three matchdays.
The 47-year-old former striker, who has also coached Bayer Leverkusen and Hamburg SV, had rescued Stuttgart from relegation in 2011 and steered them to the Europa League the next season.
He celebrated his biggest success at the club when he helped them reach the German Cup final last season, only to lose to treble winners Bayern Munich.
Stuttgart sports director Fredi Bobic said the change was needed as the team's confidence had taken a hit.
"We came to a solution which we think is great," said Bobic, who was sat next to Schneider. "This is the right step to unblock a team that has a lot of quality. Unfortunately we lost our belief a bit in recent days."
The team's bad start to the season also extended to the Europa League where Stuttgart lost 2-1 to Croatia's Rijeka in the playoff first leg last week.
(Reporting by Karolos Grohmann; Editing by John O'Brien and Toby Davis)
