Danish players were in tears as medical staff tried to revive the Inter Milan player, who suddenly collapsed near the touchline.
"The UEFA EURO 2020 match in Copenhagen has been suspended due to a medical emergency," UEFA said in a short statement.
The Inter midfielder fell to the ground with no other player around him shortly before half-time in the goalless Group B clash in Copenhagen.
Eriksen's team-mates and referee Anthony Taylor called for immediate help from medical officials, who raced onto the pitch to treat the 29-year-old.
The players formed a protective barrier around Eriksen while efforts were made to resuscitate him. Players from both teams were in notable distress on the field, as were supporters watching from the stands.
The previously raucous crowd at the Parken Stadium in the Danish capital fell silent after the 29-year-old fell to the ground near the end of the opening period, with his teammates gathering around him.
After around 15 minutes Eriksen was stretchered off the field followed by the rest of the Denmark team, while Finland's players also left the pitch.
The fans in the stadium, who were celebrating the chance to see their national team again live at the stadium, sat silently in their seats waiting for news of Eriksen's condition to filter through.