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
The 25-year-old will be assessed again next week, the ECB said in a statement.
Fast bowlers Steven Finn and Jake Ball and leg-spinner Adil Rashid have been included in the squad for the third of the four Tests against Pakistan, which begins on Aug. 3 at Edgbaston.