The 21-year-old is not expected to be included in Mark Robins' squad for Saturday's home league game against Sky Bet Championship leaders Burnley.
Huddersfield professional development coach Steve Eyre told the club's official website: "Harry is a player I know very well.
"I worked with him at Manchester City for over a decade and gave him his Football League debut during my time as manager of Rochdale. Harry is a striker with the desire to match his talent.
"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 yet to make the first-team breakthrough at the Etihad, but has had previous loan spells at Rochdale, Preston, Oldham, and Crewe, while he made two appearances for Sheffield United during a stint there earlier this season.