The 21-year-old will train with Huddersfield's youth side initially, but he could feature for the Championship outfit's first team before his stay ends on January 6.
Huddersfield professional development coach Steve Eyre told the club's official website: "It is difficult to break into the first team at Manchester City, so it makes perfect sense for everyone for us to take a closer look at him throughout the festive period.
"Although Harry will work with our Under-21 group upon his arrival, his presence will also allow first-team manager Mark Robins to see him at close quarters.
"It's a great opportunity for him to make his mark here and provide more competition in the playing group."
Bunn has had previous loan spells at Rochdale, Preston North End, Oldham Athletic, Crewe Alexandra and Sheffield United.