Eriksen fell to ground when receiving a throw-in with no other player around him in the 40th minute of the Group B opener, prompting his teammates to immediately call for medical assistance.
The 29-year-old was given CPR on the pitch during a lengthy spell of treatment, with players visibly concerned and forming a human shield to prevent the incident from being filmed.
The match was eventually postponed, and UEFA have now confirmed that the two teams have held a "crisis meeting" to determine what to do next.
A further announcement is expected at 6.45pm BST, but UEFA have revealed that the playmaker has been taken to hospital and has been "stabilised".
The Danish Football Association have also confirmed that Eriksen is conscious and now undergoing further examinations to determine the cause and extent of the issue.
"Christian Eriksen is awake and is undergoing further examinations at Rigshospitalet," they said on Twitter.
Group B also features Belgium and Russia, who are due to face each other at 8pm. body check tags ::