Chelsea boss Jose Mourinho values Belgium playmaker Eden Hazard at £200m after reported interest from Real Madrid.
Alan Pardew is weighing up chasing a big-name summer signing to boost Crystal Palace's profile.
"We think we've found a great solution," said Stuttgart's director of sport Fredi Bobic at a press conference.
"This was the right step to unblock this team, which have a great deal of quality.
"Unfortunately, we had lost a little belief in recent times. We are all convinced by this solution."
Stuttgart started the season with high expectations, despite struggling to avoid relegation last term.
Reaching the final of the DFB-Pokal was widely seen as the only achievement which kept Labbadia in his job for so long as their league struggles kept him under pressure.
But with a place in the Europa League hanging in the balance following a 2-1 defeat to Rijeka last Thursday, Bobic said they had to act to avert the worst.
"The team seems like it had lost a bit of its appetite," Bobic said. "The contact with the team was getting further and further apart.
"I've been to speak to the team myself and told them that now's the time we released the hand brake.
"It was not an easy decision."
Stuttgart have promoted from within with Schneider leaving his post as under-17s coach to take charge of the first team three days ahead of their pivotal Europa League return leg against Rijeka.
"I'm a little nervous because there are a few more people here than there are for my under-17 press conferences," said Schneider.
"But I'm very positive that we will get the job done with my coaching team. I'd like to thank the club for the faith they have shown in me."