The 20-year-old forward, who was born and raised in Stockholm, was injured Thursday when he was hit in the face by a puck that was shot from the point and deflected off the crossbar.
"It was just a freak accident after practice; he was in the corner and there was a shot that went to the net and it hit the crossbar and inadvertently hit him," coach John Hynes said. "He has a fracture and no surgery is needed, so that's good news. He should be able to continue his physical activity over the course of that time and he'll be back ready to go when that time comes."
The Devils open their season against the Edmonton Oilers at Scadinavium on Saturday (1 p.m. ET; NHLN, SN, MSG+, NHL.TV) as part of the 2018 NHL Global Series Challenge.
"It stinks because he's had a great training camp," New Jersey forward Travis Zajac said. "He was playing better than how he started last year, but he'll get a chance to come back even stronger. It's one of those things as a young guy you just have to take in stride, not let it bother you, and just make sure you're prepared to contribute when you do come back."
Bratt had 35 points (13 goals, 22 assists) in 74 games as an NHL rookie last season. The Devils selected him in the sixth round (No. 162) in the 2016 NHL Draft.
"I met up with him right away after practice Thursday, and you feel so bad for him," said forward Marcus Johansson, a native of Landskrona, Sweden. "This is once-in-a-lifetime thing to play an NHL game in Sweden and having family and friends here. He was playing really well, too, and working hard all summer.
"It's not a fun situation and he's not happy right now, but he's a young kid and he has a lot of hockey ahead of him, so you don't want to risk anything by coming back too soon."
Stefan Noesen played right wing on the line with center Pavel Zacha and Johansson in Bratt's absence during practice Friday.
The Devils agreed to terms with Drew Stafford on a one-year contract worth $810,000 on Friday. The 32-year-old forward was in training camp with New Jersey on a professional tryout offer.
"Drew is a fantastic veteran player and was a strong part of our team and part of our success last year," Hynes said. "He's one of these guys who understands where he's at in his career, and we feel like there's attributes to him as a player that really help our team."
Stafford has 15 points (eight goals, seven assists) in 59 games last season, his first with New Jersey. He has 415 points (191 goals, 224 assists) in 784 NHL games.