The midfielder went to ground during the match and required extensive on-pitch treatment towards the end of the first half of the game in Copenhagen
The 29-year-old Inter Milan player's condition has "stabilised", according to tournament organisers Uefa.
The game in Copenhagen was suspended before half-time after the former Spurs playmaker fell to the ground and was given emergency treatment on the field.
Finland won the Group B match 1-0 after it restarted.
Danish players were applauded on to the pitch by their opponents as they returned to the field to resume the game.
Denmark midfielder Christian Eriksen is stable in hospital after collapsing during his country's opening Euro 2020 game against Finland in Copenhagen.
The Inter star went down during the opening half of the Group B match and required extensive medical attention on the pitch before he was removed on a stretcher.
After Eriksen was taken to the hospital, UEFA sent out word that his condition was stable. The Danish FA also confirmed that Eriksen was awake and undergoing further tests. The game was initially suspended before it was later restarted after a delay of more than 90 minutes, with Finland winning 1-0.
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What was said?
UEFA provided the first update on Eriksen's status, saying in a tweet: "The player has been transferred to the hospital and has been stabilised."
The Danish FA also sent out a tweet saying: "Christian Eriksen is awake and is undergoing further examinations" at the hospital.
Eriksen's agent Martin Schoots told Dutch radio station NPO Radio 1 that Eriksen was awake, saying: "I've been in contact with his father for a while and he says that Christian is breathing and can talk, that's the good news. He is conscious, but everyone is in shock. His girlfriend is with him.”
Play came to a halt just before half-time as Eriksen, without any players around him, dropped to the ground.
Referee Anthony Taylor immediately blew his whistle and brought proceedings to a halt. Denmark and Finland immediately called for the medical staff, who raced onto the pitch to administer treatment.
His Danish team-mates formed a shield around him as the medics provided treatment, before white sheets were held up around him to provide privacy.
Following several minutes of on-field treatment, UEFA announced that the match was suspended. The European governing body said just over an hour later that following a request from both teams' players, the match would be resumed.
The 29-year-old came up through Ajax's academy before going on to become a star for the Dutch giants.
Eriksen's exploits in the Netherlands earned him a move to Tottenham in 2013, where he would go on to become one of the north London club's top players.
After six and a half seasons with Spurs, Eriksen moved to Inter in January 2020.
Eriksen took time before becoming a key figure in Milan, but was a major part of Antonio Conte's 2020-21 Serie A title winners.
Saturday's other Group B game between Belgium and Russia took place as scheduled at 20:00, with Belgium winning 3-0.
Belgium striker Romelu Lukaku, who scored twice, paid tribute to his Inter team-mate on opening the scoring, saying to the TV cameras "Chris, I love you".
Three matches will be played today. Austria Vs North Macedonia, England Vs Croatia and Netherlands Vs Ukraine