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
Joshi, who took 110 wickets for India in 15 Tests and 69 one-day internationals from 1996-2001, had already began working with the bowlers ahead of the first Test starting in Dhaka on Sunday, the Bangladesh Cricket Board told local media.
The BCB had hoped to appoint former Australia legspinner Stuart MacGill but talks failed to produce a deal.
Bangladesh face Australia in a Test match for the first time since 2006. The second Test starts in Chittagong from Sept. 4.