The Inter Milan midfielder collapsed towards the end of the first half, and received treatment from medics as his teammates gathered in a wall around him.
The BBC live coverage continued to focus on Eriksen receiving CPR for several minutes, and also showed his wife being comforted by teammates and officials.
Eventually the live coverage from the Parken Stadium in Copenhagen cut back to the studio, where a visibly shaken host Gary Lineker offered his words of prayer for Eriksen, along with pundits Cesc Fabregas, Alex Scott and Micah Richards.
But viewers were angry with the decision to keep broadcasting during the harrowing incident.
The Ofcom rules on privacy say: “Broadcasters should not take or broadcast footage or audio of people caught up in emergencies, victims of accidents or those suffering a personal tragedy, even in a public place, where that results in an infringement of privacy, unless it is warranted or the people concerned have given consent.”
The Group B match was suspended just before half-time, and resumed at 19.30 BST.
Viewer reaction to the coverage
Colin Millar tweeted: “Denmark's players had to form a protective ring around their teammate. A distraught wife was broadcast to the world. TV broadcasters and cameramen are capable of blocking footage of pitch invaders, but not this? Sorry, that is not ok.”
@JoeyTHFC referred to the Ofcom rules and added: “This is what OFCOM say about situations such as we’ve just experienced. One that was ignored for a good 10-15 minutes, especially by showing footage of Eriksen’s wife. Shame on you, BBC.”
@Siobhan3Leigh posted: “So much respect for these that surrounded Eriksen on the floor.. but it’s truly disgusting that the BBC found it appropriate to film a man on the floor receiving CPR and his devastated wife!!! Sending all my love and healing to Eriksen and his family”
Others simply recorded their shock. Fabrice Muamba, the former footballer who recovered after suffering a cardiac arrest in 2012, tweeted: “Please God.”
Uefa later posted the following statement: “Following the medical emergency involving Denmark's player Christian Eriksen, a crisis meeting has taken place with both teams and match officials and further information will be communicated at 19:45 CET. The player has been transferred to the hospital and has been stabilised.”