Speaking at a media briefing on Wednesday, DBU president Jesper Moeller said that he was angered by FIFA's actions and that the association had ruled out voting for Infantino in next year's election.
"There is only one candidate, and we'll have to see if there's another candidate, there is still time, but Denmark will not be supporting the current president," he said.
"This situation is quite extraordinary. I'm not just disappointed, I'm angry. This is my seventh finals... It is that the players have to be exposed to this is completely unacceptable. We have to respond to it," Moeller added.
Jakob Jensen, CEO of the DBU, outlined the communication that the association had with the governing body, telling them before the tournament that they intended to wear the armband in support of diversity.
Jensen said that the English FA was then expressly told at a meeting that the team captain might receive a yellow card for wearing the armband.
"We were told that at the very least we would get a yellow card. It has been discussed whether there was any authority to give us a yellow card at all. It is there. We could have got a yellow card, we could have been suspended," he told a news conference at the team's training base.
Media reports surfaced on Wednesday following the news conference that DBU president Jesper Moeller had said the FA was considering pulling out of the governing body for world football after Denmark and six other European teams were threatened with sporting sanctions if they wore the armband.
"Some media have made the misunderstanding that DBU will withdraw from FIFA," DBU head of communications Jakob Hoejer told Reuters in a WhatsApp message.
"That was not said at the press conference. We're critical and not satisfied and we'll not vote for the present FIFA-president (Gianni Infantino). We will discuss further actions with our Nordic and European colleagues."
Denmark face France in their second Group D game on Saturday.
