Musacchio was attempting to evade a Diego Castro challenge after coming on as a second-half substitute on Sunday, when he planted his left foot in the turf, resulting in his lower leg snapping.
A statement from Villarreal confirmed that the Argentinian had an operation in Madrid, which has been deemed a success.
The club has not given a timescale for Musacchio's return, but he is certain to miss the rest of the season, while any hope he had of representing his country in this year's Copa America have also been ended.
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