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
Anderson, who is England's all-time leading Test wicket-taker, sustained a stress fracture during the home series against Sri Lanka in June, though he did play three Tests against Pakistan in July and August.
England are likely to announce his replacement on Thursday, the BBC reported.
England play three one-day internationals beginning on Oct. 7 followed by Tests in Chittagong from Oct. 20 and Dhaka from Oct. 28 before they begin a tour of India, which includes five Tests with the first starting on Nov. 9.