The integration of process planning and scheduling is important for an efficient utilization of manufacturing resources. However, the focus of existing works is mainly on deterministic constraints of jobs. This article proposes a novel memetic algorithm for the integrated process planning and scheduling problem with processing time uncertainty based on processing time scenarios. First, a mathematical model for the stochastic integrated process planning and scheduling problem based on the network graph is established. Due to the nonlinearity in the model and the complexity of the problem, a memetic algorithm is then suggested for this problem. A novel local search (variable neighborhood search) algorithm is incorporated into the memetic algorithm. Two effective neighborhood structures are employed in the variable neighborhood search algorithm to improve the overall performance of the population. Furthermore, for the uncertainty in processing times, a set of scenarios have been generated to evaluate each individual. Finally, two performance measures—the expected performance measure and the worst-case deviation measure—are introduced and compared. In the experimental studies, the proposed memetic algorithm is tested on typical benchmark instances. Computational results show that the expected makespan measure performs better than the worst-case deviation measure and the proposed method exhibits high performance especially for large-scale instances. In addition, the results obtained by the proposed memetic algorithm are more satisfactory than those obtained by the algorithm that considers deterministic processing times only.