Kodjia first suffered the ankle injury against Blackburn Rovers last season, and had an operation at the end of the season. The 28-year-old returned for 20 minutes against Middlesbrough in September, and started the following seven second-tier fixtures.
The forward suffered a recurrence of the issue against Birmingham City last month, before causing further damage while on international duty with Ivory Coast.
"The operation will be done probably later this week," Bruce told reporters in a press conference. "It's the worst possible news that we can have, but it's football.
"We've been dealt some cruel ones over the last few weeks with [John] Terry and Kodjia, and obviously [Jack] Grealish, [Henri] Lansbury and [Mile] Jedinak and we've managed to cope so hopefully we'll manage to cope until January and then we'll see if we can do something to try and help the squad.
"You don't have to spend millions. It's always a bit more difficult to loan a player, but that's where we are and that's what we're looking at."
Villa play Ipswich Town on Saturday with the chance to keep their place in the Championship playoffs.