Manager Eddie Howe confirmed the centre-back will be out for an estimated four to six weeks following the incident.
Burn suffered rib injuries and a punctured lung after a tackle from Nordi Mukiele during the first half. Despite initially managing to continue, he was eventually withdrawn from the match.
Reports indicate he struggled to breathe in the changing rooms, prompting a hospital visit for further assessment.
Howe spoke to the media ahead of Newcastle's Carabao Cup tie against Fulham, acknowledging the significant impact Burn's absence will have on the squad.
At a minimum, the defender is expected to miss the Carabao Cup clash with Fulham, Premier League fixtures against Chelsea, Manchester United, Burnley, Crystal Palace and Leeds United, as well as the FA Cup third-round match at Bournemouth.
"I was sort of under the radar really in terms of reviewing the game, the importance of Dan and losing him just for everything that he brings to the team. That was a big blow for us," said Howe.
"I think he's been excellent in recent weeks. So yeah, it's a rib problem with some issue with his lungs.
"We wish him well. It will probably be around four to six weeks."
Depending on the pace of his recovery, Burn could also miss further matches, including the Premier League games against Wolves and Aston Villa, as well as Newcastle's Champions League tie with PSV Eindhoven.
The defender's return is tentatively expected by mid-January, though the club will monitor his progress closely before confirming any potential involvement later in the month.