Casteels leapt high to try and catch the ball in the penalty area and his knee caught Gentner in the face in the process.
"Extensive examinations revealed that Christian Gentner had suffered breaks to the lower and lateral (parts of his) eye-socket, his nose and his upper-jaw," said Stuttgart in a statement.
"The 31-year-old will undergo surgery over the next few days and is expected to make a complete recovery."
Stuttgart's sporting director Michael Reschke described it as a "cruel blow" for Gentner.
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"The most important news though is that he will make a full recovery," he added.
"Christian is enormously important for us both on, as well as off, the pitch. In the four Bundesliga games we’ve played thus far, he has impressively proven his exceptional qualities."
Wolfsburg have wished Gentner a speedy recovery but could not immediately be reached for further comment. Belgian goalkeeper Casteels has yet to comment.
The incident caused controversy because the referee waved play on and did not consult the video assistant to see whether Casteels had committed a foul. Video referees are being trialled in the Bundesliga this season.
(Writing by Brian Homewood in Milan; Editing by Rex Gowar)
