Hogg had to be carried from the field on a stretcher after requiring 14 minutes of treatment following a collision with team-mate Mark Hudson in the first half of Friday's 4-0 defeat.
The 28-year-old was taken to hospital for treatment before being discharged on Saturday, with no significant trauma to any of the soft tissues in his neck.
A statement read: "Although he is expected to miss the rest of the 2016/17 season, the Club is happy that Jonathan is in no immediate danger and looks forward to seeing 'Hoggy' back out on the pitch as soon as is safely possible.
"Alongside Jonathan, everyone at the Club would like to thank the medical staff at Bristol City and the NHS staff at Bristol Royal Infirmary for ensuring Jonathan was looked after and received appropriate care."
Hogg has made 30 appearances this season to help Huddersfield to third in the Championship table.