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Buttler sustained the knock while keeping wicket in Australia's first innings in the drawn fourth Test at the Sydney Cricket Ground.
The 31-year-old will now fly home, with Sam Billings in line to make his Test debut behind the stumps in Hobart from Friday.
"Jos Buttler is going to be going home," Root said at the post-match presentation.
"It's quite a bad injury, so it's a really disappointing shame for him and for the team but it's part and parcel of playing Test cricket, sometimes you've got to take these things.
"And the way he stood up throughout the rest of the game having taken that and put in for the boys is testament to his character and how much he cares about playing for this team."
Ben Stokes and Jonny Bairstow are also doubts ahead of the fifth Test, having sustained injuries. All three batted on Sunday as England dug deep to draw on the final day at the Sydney Cricket Ground.
Australia had led the series 3-0, with their hopes of a 5-0 sweep now ended.
"It's been a difficult tour, but we stood up and found a way to get a result out of this game," added Root.
"We wanted to put pride back into the badge. The way we went about it in this game, we did that. We know there's a long way to go. It would be nice to front up again next week and go one better."