Former Tottenham star Eriksen collapsed shortly before half-time in Denmark's opening Euro 2020 game against Finland on Saturday.
The 29-year-old Inter Milan player had emergency medical treatment on the pitch before being taken to hospital.
"His condition is stable and he continues to be hospitalised for further examination," said a statement.
"This morning we have spoken to Christian, who has sent his greetings to his team-mates.
"The team and staff of the national team has received crisis assistance and will continue to be there for each other after yesterday's incident.
"We would like to thank everyone for their heartfelt greetings."
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