The announcement noted that Reigns and Wyatt are dealing with "medical issues", which prompted the changes just two days before the pay-per-view.
On Friday, it was revealed that Angle will be replacing Roman Reigns at the upcoming WWE TLC: Tables, Ladders and Chairs event.
Wyatt has been replaced by SmackDown's AJ Styles, who will meet Finn Balor in a one-on-one match.
In a statement to ESPN, a WWE representative said, "We have confirmed that three of our performers have been diagnosed with a viral infection".
Pro Wrestling Torch has reported that WWE wrestlers are being tested for viral meningitis, a disease that might be effecting several people on the roster.
Our sources say the creative team learned about the possibility of Roman/Bray not being able to wrestle late in the week and came up with a plethora of replacement options, with Kurt Angle returning seemingly being the best one. Angle will be replacing Roman Reigns in the main event TLC match that was originally set to pit the newly reunited Shield against the team of The Miz, Sheamus, Cesaro, Braun Strowman, and the recently returned Kane. He was inducted into the WWE Hall of Fame in the same month. Same for AJ vs. Finn. His last-minute return is in many ways a double-edged sword for fans in that it provides increased intrigue this weekend but doesn't have the expected build and fanfare WWE would've preferred for such a momentous occasion.