Considering both process planning and shop scheduling in manufacturing can fully utilize their complementarities, resulting in improved rationality of process routes and high-quality and efficient production. Hence, the study of Integrated Process Planning and Scheduling (IPPS) has become a hot topic in the current production field. However, when performing this integrated optimization, the uncertainty of processing time is a realistic key point that cannot be neglected. Thus, this paper investigates a Fuzzy IPPS (FIPPS) problem to minimize the maximum fuzzy completion time. Compared with the conventional IPPS problem, FIPPS considers the fuzzy process time in the uncertain production environment, which is more practical and realistic. However, it is difficult to solve the FIPPS problem due to the complicated fuzzy calculating rules. To solve this problem, this paper formulates a novel fuzzy mathematical model based on the process network graph and proposes a MultiSwarm Collaborative Optimization Algorithm (MSCOA) with an integrated encoding method to improve the optimization. Different swarms evolve in various directions and collaborate in a certain number of iterations. Moreover, the critical path searching method is introduced according to the triangular fuzzy number, allowing for the calculation of rules to enhance the local searching ability of MSCOA. The numerical experiments extended from the well-known Kim benchmark are conducted to test the performance of the proposed MSCOA. Compared with other competitive algorithms, the results obtained by MSCOA show significant advantages, thus proving its effectiveness in solving the FIPPS problem.