Eriksen collapsed during Denmark's opener against Finland in June, with Kjaer the first on the scene to place his team-mate in the recovery position before leading his side to form a protective screen while the Inter man received treatment.
The 29-year-old was subsequently taken to hospital, where he was fitted with a pacemaker before returning home, though it remains unclear if he will ever play again, despite visiting Inter's training ground in August.
For Kjaer's exemplary leadership, the centre-back – along with eight medics – have been hailed as the "true heroes of Euro 2020" and presented with the award by UEFA President Aleksander Ceferin.
"This year, the President’s Award transcends football," Ceferin said.
"It serves as an important and eternal reminder of just how precious life is and puts everything in our lives into the clearest perspective.
"I would also like to send my very best wishes to Christian Eriksen and his family as he continues his recovery."
After Kjaer had performed the initial CPR, the medical team responded quickly, resuscitating Eriksen before taking him off the pitch on a stretcher to rush him to hospital.
"We rushed to the field to help [Christian] and to do our job," said Mogens Kreutzfeldt, chief medical officer for Euro 2020 in Copenhagen.
"We did what we should, what we were taught, what we were trained to do.
"Everybody knew their role, everybody knew what to do.
"We were not emotional at the scene. Afterwards, we were, of course, like everybody. We're very happy and proud of the outcome."