The 29-year-old midfielder suffered cardiac arrest in his side's defeat by Finland in Copenhagen on Saturday.
The ICD - implantable cardioverter defibrillator - is "necessary due to rhythm disturbances", Danish team doctor Morten Boesen said.
Eriksen remains in hospital but says he is "fine under the circumstances".
"Christian has accepted the solution and the plan has moreover been confirmed by specialists nationally and internationally who all recommend the same treatment," added Boesen.
"We encourage everybody to give Christian and his family peace and privacy."
Former Spurs player Eriksen, who is now at Inter Milan, collapsed shortly before half-time against Finland and needed to be resuscitated with a defibrillator.
German doctor Jens Kleinfeld, who treated him on the field, told Funke media group: "About 30 seconds later, he opened his eyes and I could talk to him directly.
"That was a very moving moment, because in such medical emergencies in everyday life, the chances of success are much lower."
Kleinefeld said he asked Eriksen, "Well, are you back with us?"
The doctor said Eriksen answered, "Yes, I am back with you" and, "Damn, I'm only 29 years old".
Kleinefeld added: "That's when I knew the brain wasn't damaged and he had fully returned."
Denmark's next game is against Belgium on Thursday (17:00 BST) when they return to the Parken Stadium, which was the scene of Eriksen's collapse.
Belgium intend to kick the ball out of play in the 10th minute to take part in a minute's applause for Eriksen, with Danish fans planning the gesture as a show of support.
