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
Star all-rounder Shakib Al Hasan and batsman Nasir Hossain have been dropped from the 15-member squad announced on Monday.
Bangladesh's tour of South Africa will kick off on Sept 28 with the first Test in Potchefstroom. The second Test starts on Oct 6 in Bloemfontein.
The tigers will also play three ODIs and two T20 matches during the tour.
Bangladesh Test Squad:
Mushfiqur Rahim(c), Tamim Iqbal, Soumya Sarkar, Imrul Kayes, Sabbir Rahman, Mahmudullah, Liton Das, Mehidy Hasan, Taijul Islam, Mustafizur Rahman, Rubel Hossain, Shafiul Islam, Taskin Ahmed, Subashis Roy, Mominul Haque.