In recent years, Internet-wide scanning has attracted interest as a countermeasure against Internet-of-Things (IoT) security problems that can detect security holes. Despite the usefulness of Internet-wide scanning, it suffers from the problem of network congestion that occurs when numerous port scanning packets are used. Network congestion becomes increasingly severe in networks with limited bandwidth such as wireless networks. Therefore, port-scanning packets must be sent at long intervals when scanning such networks. In contrast, an inappropriate reduction of scanning speed increases the time required to complete scanning, making it difficult to scan IoT devices comprehensively before cyber-attackers identify vulnerabilities. However, setting appropriate scanning speeds is a challenge owing to the lack of a method for quantifying the impact of scanning traffic on the target network. In this study, we construct a novel analytical model to quantify the impact of scanning traffic on IoT data throughput in a target wireless LAN. The validity of our proposed model is evaluated through Monte Carlo simulations whose results demonstrate that our model is effective in approximating the impact of scanning traffic on IoT data traffic. This study contributes to overcoming a key shortcoming of Internet-wide scanning as a critical factor in efficient probing.