Tait, a key figure in Australia's World Cup win in the Caribbean earlier this year, had been recovering from elbow surgery and medical staff said there would be insufficient time for him to be fit for the Sept. 11-24 tournament in South Africa.
"This news is very disappointing for Shaun Tait after such a successful World Cup campaign and I know he was looking forward to being part of the first ICC World Twenty20," chairman of selectors Andrew Hilditch said.
"The flip side is that this presents a great opportunity for a good young fast bowler who had such a good season last year," he added.
Hilditch said the 24-year-old Tait's target was to make the seven-match one-day series in India starting at the end of September.
Tasmania paceman Hilfenhaus, also 24, has appeared in one one-day international and one Twenty20 match for the Australians.