The former Tottenham playmaker dropped to the ground at the Parken Stadium shortly before half-time of the Group B fixture, leaving players from both teams in clear distress.
English referee Anthony Taylor immediately called medics on to the pitch and Eriksen underwent prolonged treatment with compressions performed on the chest of the Inter Milan player before he was taken to hospital.
The Danish Football Association later provided an update on the 29-year-old's condition and revealed the match would be completed on Saturday night.
A statement read: "Christian Eriksen is awake and his condition remains stable. He remains hospitalized at Rigshospitalet for further examinations.
"The match against Finland will be played tonight (Saturday). This happened after the players had it confirmed that Christian is okay. The match resumes at 20.30 (19.30 BST)."
UEFA confirmed players from both sides requested the Group B encounter be finished, which was goalless just before half time.
"Following the request made by players of both teams, UEFA has agreed to restart the match between Denmark and Finland tonight at 20:30 CET," a statement said.
"The last four minutes of the first half will be played, there will then be a five-minute half-time break followed by the second half."
BBC had shown the fixture and issued an apology after images of Eriksen receiving treatment were broadcast before the programme was brought to a premature end.
Presenter Gary Lineker and pundits Cesc Fabregas, Alex Scott and Micah Richards all appeared in total shock when footage cut back to the studio with Scott visibly emotional when asked about the incident.
In a statement, a BBC spokesperson said: "Everyone at the BBC is hoping Christian Eriksen makes a full recovery.
"We apologise to anyone who was upset by the images broadcast.
"In-stadium coverage is controlled by UEFA as the host broadcaster, and as soon as the match was suspended, we took our coverage off air as quickly as possible."
Eriksen collapsed face first as he rushed to receive a throw-in close to the corner flag deep in Finland's half and team-mates formed a shield around the midfielder while he received treatment.
After he was carried off the pitch on a stretcher, the fans inside the stadium in Copenhagen chanted Eriksen's name in a moment of unity.
UEFA president Aleksander Ceferin said: "Moments like this put everything in life into perspective. I wish Christian a full and speedy recovery and pray his family has strength and faith.
"At these times, the unity of the football family is so strong and he and his family carry with them the good wishes and prayers of everyone.
"I heard of fans of both teams chanting his name. Football is beautiful and Christian plays it beautifully."
Eriksen's club side Inter Milan said on Twitter: "Forza Chris, all of our thoughts are with you" and former team Tottenham added: "Get well soon Christian. The whole Spurs family is with you."
Denmark's fixture with Finland resumed after an almost 90-minute delay with the teams welcomed back onto the Parken Stadium pitch to warm applause.
England, who get their Euro 2020 campaign under way on Sunday against Croatia, were due to hold a press conference at 6.30pm BST with captain Harry Kane set to be alongside manager Gareth Southgate.
Kane spent eight seasons with Eriksen at Tottenham and the media briefing was cancelled at the request of the Football Association.
A statement on the live feed read: "In light of the awful events unfolding in Copenhagen, the FA have asked permission not to do their press conference scheduled at 19.30 CET. So the ENG press conference is cancelled. Thank you for your understanding."
Southgate later added: "We are encouraged by the update from the Danish Football Association this evening. On behalf of the FA , our players and staff, we send our very best wishes to Christian and those close to him.
"We pay tribute to those who went to his aid with such care to give the support he received. Our thoughts remain with Christian and his family tonight."
The FA also said in a statement "Our thoughts this evening are with Christian Eriksen and his family, and all connected with the Danish Football Union."
Inter team-mate Romelu Lukaku paid tribute to Eriksen after he scored for Belgium against Russia in Saturday evening's other Euro 2020 match.
He said to the pitchside camera: "Chris, I love you" after he broke the deadlock in the Group B clash.