Abstract In contrast to a conventional virtual machine (VM), a container is a lightweight virtualization technology. Containers are becoming a prominent technology for cloud services because of their portable, scalable, and flexible deployments, especially in the Internet of Things (IoT), smart devices, and fog and edge computing. It is a type of operating system‐level virtualization in which the kernel allows multiple isolated containers to run independently. Container placement (CP) is a nontrivial problem in Container‐as‐a‐Service (CaaS). CP is mapping to a container over virtual machines (VMs) to execute an application. Designing an efficient CP strategy is complex due to several intertwined challenges. These challenges arise from a diverse spectrum of computing resources, like on‐demand and unpredictable fluctuations of IT resources by multiple tenants. In this article, we propose a modified sum‐based container placement algorithm called a multi‐objective optimization‐based container placement algorithm (MSBCPA). In the proposed algorithm, we have considered two metrics: makespan and monetary costs for optimizing available IT resources. We have conducted comprehensive simulation experiments to validate the effectiveness of the proposed algorithm over the CloudSim 4.0 simulator. The proposed optimization algorithm (MSBCPA) aims to minimize the makespan and the execution monetary costs simultaneously. In the simulation, we found that the execution cost and energy consumption cost reduce by 20% to 30% and achieve the best possible cost‐makespan trade‐offs compared to competing algorithms.