The Danish Football Union added that Inter Milan midfielder Eriksen was "awake" and set for "further examinations" after he fell to the ground with no other player around him during the first half of the match in Copenhagen.
Team-mates and referee Anthony Taylor called for immediate help from medical staff, with the players forming a protective barrier around Eriksen while efforts were made to resuscitate him.
UEFA soon confirmed the match had been suspended because of "a medical emergency", and would be completed later in the day.
UEFA's statement read: "[After] the medical emergency involving Denmark's player Christian Eriksen, a crisis meeting has taken place with both teams and match officials and further information will be communicated at 19:45 CET.
"The player has been transferred to the hospital and has been stabilised."
The match resumed later, with Finland claiming an historic 1-0 victory in its first match at a major tournament.
Eriksen was sent messages from around the football world on social media after the concerning incident.
Former club Tottenham Hotspur – where he spent six and a half years – posted on Twitter: "All of our thoughts are with Christian Eriksen and his family."
Harry Kane played with Eriksen at Spurs and had been due to face the media alongside England manager Gareth Southgate on the eve of their meeting with Croatia at Wembley.
The news conference was cancelled and the Football Association said: "Our thoughts this evening are with Christian Eriksen and his family, and all connected with the Danish Football Union."