Denmark coach Morten Olsen said after the World Cup qualifier: "Our first thoughts are for Jacobsen who went to the hospital.
"We hope he can return home with the team."
The shoulder injury is another blow for the defender, who was limited to just seven appearances for German club Nurnberg last season because of injury problems.
Everton manager David Moyes had pencilled Jacobsen in to make his debut against Stoke on Sunday.
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