Chung, whose physical presence and versatility has been an important part of the Patriots' impressive start on defense this season, had been limited all week with a heel injury.
Meanwhile, Burkhead had been limited with a foot injury and his absence means that Sony Michel and James White stand alone atop the running back depth chart. Veteran Brandon Bolden and rookie Damien Harris are top backups who could possibly be in line to take on expanded roles Sunday.
Core special teamer Nate Ebner (groin) has also been ruled out.
The Patriots also don't plan to activate veteran tight end Benjamin Watson before Saturday's 4 p.m. ET deadline, a source tells ESPN's Field Yates. Watson had served a four-game NFL suspension to open the season, and the Patriots have a roster exemption for him until Monday at 4 p.m. ET.