Rizwan and Irfan both suffered hamstring injuries in the third match in Rawalpindi, where a second-string New Zealand side won by seven wickets to level the five-match series 1-1
Nasir returns to the fold after almost a two-year hiatus. He played the last of his 17 Tests against South Africa in 2015.
Pacer Shafiul’s made his last appearance against England in October last year.
Bangladesh Cricket Board chief selector Minhajul Abedin announced the squad on Saturday at Mirpur’s Sher-e-Bangla National Cricket Stadium.
The first game of the two-Test series will begin on Aug 27 in Dhaka.
Bangladesh squad for first Australia Test:
Tamim Iqbal, Soumya Sarkar, Imrul Kayes, Mushfiqur Rahim, Shakib Al Hasan, Mehedi Hasan Miraz, Sabbir Rahman, Mossadek Hossain, Mustafizur Rahman, Liton Das, Shafiul Islam, Taijul Islam, Taskin Ahmed, Nasir Hossain.