Queensland's Kasprowicz, 31, has not added to his 18 one-day caps since playing against India in Bangalore on November 12.
Bichel, also from Queensland, took 16 wickets at an average of 12.31 in last year's World Cup but has struggled in the current triangular series with figures of 3-197 from six matches.
Kasprowicz has taken 11 wickets in the Australia interstate one-day competition in 2003-04 at an average of 15.81 including 4-19 against Tasmania in Hobart on January 26.
Simon Katich has been retained while Mike Hussey, who made 17 not out in his debut against India in Perth on Sunday, has been dropped.
Out-of-form batsman Damien Martyn, who has made 122 runs at 17.42 in the triangular series, has been retained.
The right-hander has scored just three runs in four matches against India in the series.
Australia chairman of selectors Trevor Hohns said in a statement: "It is fair to say that Andy Bichel has not been bowling as well as we would like and we feel that a spell at state level might help him recapture his form.
"Michael Kasprowicz deserves this opportunity. We were impressed with his work on the recent one-day tour of India."
Australia will host India for the best-of-three finals series starting in Melbourne on Friday, followed by a second match in Sydney on Sunday and a third, if required, in Brisbane two days later.
India play Zimbabwe in Perth on Tuesday in the final match of the triangular series. The Africans are without a win after seven matches in the series.
Australia will begin a one-day and test tour of Sri Lanka later this month.
Australia: Ricky Ponting (captain), Adam Gilchrist, Michael Clarke, Jason Gillespie, Ian Harvey, Matthew Hayden, Brad Hogg, Michael Kasprowicz, Simon Katich, Brett Lee, Damien Martyn, Andrew Symonds, Brad Williams.
