The shooting happened on Peridot Fold, in Fartown, on November 11. No-one was injured.
At the time Detective Inspector Mark Atkinson, of the Firearms Prevent Team, said he believed it was a "targeted attack".
A 34-year-old man and a 32-year-old woman, both from Huddersfield, have now been arrested in connection with the incident.
Police have said the investigation remains ongoing and anyone with information can contact them on 101 or Crimestoppers, anonymously, on 0800 555 111.