Hopper will require an arthroscope procedure after experiencing "pain and discomfort" in his knee, having met with consultants in Melbourne this week.
Surgery is set to see Hopper placed on the sidelines for an indefinite period, with the club hoping the procedure will place the midfielder in good stead for the second half of this season.
Davis also remained in Victoria following Sunday's loss to Richmond, where he suffered a significant hamstring injury that will keep him sidelined for the coming months.
Scans have confirmed a grade three tear for the veteran defender, who is anticipated to return in the second half of the season.
A broken arm has also sidelined utility Daniel Lloyd, who sustained the setback early into the Round 2 encounter with the Tigers.
The Giants are currently without star forward Toby Greene until Round 6 due to suspension, with senior coach Leon Cameron required to move the magnets for his side's coming clash with Gold Coast on Saturday.