The Dutchman was sent to San Siro to gain some first-team experience, but he picked up an injury in his first days in Italy, which kept him sidelined.
Van Ginkel had played just 33 minutes in Serie A despite battling back from injury until he got a start against Udinese a fortnight ago and impressed in a 2-0 win.
But the 22-year-old seems to be cursed because Milan have confirmed that van Ginkel is again facing a spell on the sidelines due to an ankle injury sustained in training.
"AC Milan would like to communicate that during today's training session, van Ginkel sustained a sprained ankle with damage to the ligament capsule," a statement from the club reads.
The extent of the injury isn't known, but it is another big blow to van Ginkel, who was showing the first signs of hitting his stride in Milan.