The right-arm seamer suffered pain in his right shoulder following the first Test loss in Wellington and scans showed he had damaged a rotator cuff muscle.
A New Zealand Cricket statement said no replacement will be called into the squad for the Test starting at Hagley Oval on Saturday, meaning a place opens for either Matt Henry or Neil Wagner. The new ball pair of Trent Boult and Tim Southee is likely to be retained.
Bracewell, who has played in New Zealand’s last six Tests, took 2-127 as Australia piled on 562 in their only innings at the Basin Reserve.
“Doug has been a consistent performer for us this summer and put a lot of work into his game, so to miss out on the final Test against Australia is very disappointing for him and us,” Black Caps coach Mike Hesson said.
“He’ll be given time to recover and we’ll work with him to get him back training as quickly as possible.”
The injury is likely to keep Bracewell out of the Island of Origin Twenty20 game in Wellington on February 28.
Henry has been New Zealand’s best one-day international bowler this summer, taking 23 wickets in eight games.
However, he has largely struggled in three Test appearances, taking 10 wickets at an average just under 50.
Left-armer Wagner is a proven performer in 18 Tests, taking 67 wickets at 33.3. He took nine wickets in the two Tests against Sri Lanka before Christmas.
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