Juventus shares were down 17.7 percent at 1.39 euros at 0730 GMT after plunging almost 21 percent when trading in Milan began.
De Ligt scored Ajax's second goal as they won 2-1 in Turin to go through 3-2 on aggregate.
Juventus coach Massimiliano Allegri dismissed speculation about his future following their Champions League exit against Ajax Amsterdam on Tuesday, saying he would be at the club next season. He said: "Juventus are the favourites, especially after the Amsterdam result".
And the 19-year-old, who was not born when Ajax last reached the last four, was left stunned by what he and his team-mates had achieved.
A young Ajax team that included players who weren't born when either of the first Toy Story films were released.
Juventus and Bayern Munich are also keen on De Ligt but one source has said the Netherlands worldwide "only wants to listen to Barcelona".
In the semi-final, Ajax will meet either the Abu Dhabi-backed millionaires of Manchester City or Tottenham Hotspur - admittedly not in the same financial league as City, but still with access to the huge Premier League money pot. We know we can play and, as you can see, we are really good at the moment.
Van De Beek was on the end of further breathtaking Ajax approach play, but again Szczesny was equal to the task and tipped the ball over the crossbar.
Matthijs de Ligt celebrating Ajax's second goal in their stunning win away to Juventus.
Despite finishing second in Group E and drawing holders Real Madrid in the last 16, the Dutch side won 5-3 on aggregate - including a 4-1 win at the Bernabeu - to reach the quarter-finals.
Ajax fell behind last night but goals from Donny van de Beek...
La Repubblica lamented Juventus's continuing failed search for a third European crown; their last came in beating Ajax on penalties in the 1996 final. "It's very hard to play against us and our philosophy". De Ligt's smile spoke for itself. But not all of them score match winning goals to take their teams to the semi-finals of the Champions League.
Why might I be randomly bringing the hugely popular animated film series up?
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