The 29-year-old spent several days in hospital and had a defibrillator implanted to regulate his heartbeat after the game on June 12.
Damsgaard is more familiar than most with the Denmark coach, who handed the Jyllinge-born youngster his professional debut at Nordsjaelland in 2017.
Thomas Delaney and Kasper Dolberg starred in the match as Denmark defeated the Czech Republic 2-1 to enter the semi-finals of the ongoing Euro Cup on Saturday.
Christian Eriksen's Denmark teammates say his visit came as a big surprise and that he gave them all a hug before having lunch with the team.
The Danish soccer federation wrote on Twitter that Eriksen was released from the Rigshospitalet in central Copenhagen after a successful operation.
Denmark took an early lead in the game but Belgium launched a second-half comeback to win 2-1.
The players and spectators paid tribute to Eriksen with a minute's applause after 10 minutes at a Parken Stadium adorned with banners showing supporters' support for Denmark's star player.
The Inter Milan player had to be revived after his heart stopped in the middle a Euro match on Saturday, casting a dark shadow over his career.
Players from both teams halted play after 10 minutes as the 25,000 fans rose for a minute of thunderous applause in tribute to Eriksen.
Christian Eriksen collapsed and required CPR during Denmark's game against Finland in Copenhagen where he remains in hospital.
Medical personnel administered CPR as Christian Eriksen lay motionless on the field for about 15 minutes before being carried off the pitch and rushed to hospital.
When Eriksen collapsed, just before half-time in Saturday's game against Finland at Euro 2020, time stood still in Copenhagen.
Kasper Hjulmand's talented side know that their qualification from Group B will be in jeopardy if they get the same treatment that leaders Belgium dished out to Russia on Saturday.
Eriksen on Tuesday thanked everyone for greetings and messages and revealed that he still has to go through some examinations at hospital.
Since the incident, Morten Boesen and the Denmark medical staff have received plaudits for the way they reacted to prevent a tragedy from unfolding.