With the rapid growth of the internet of things (IoT), huge amounts of multimedia data are being generated from and/or exchanged through various IoT devices, systems and applications. The security and privacy of multimedia data have, however, emerged as key challenges that have the potential to impact the successful deployment of IoT devices in some data-sensitive applications. In this paper, we conduct a comprehensive survey on multimedia data security and privacy protection in the IoT. First, we classify multimedia data into different types and security levels according to application areas. Then, we analyse and discuss the existing multimedia data protection schemes in the IoT, including traditional techniques (e.g., cryptography and watermarking) and emerging technologies (e.g., blockchain and federated learning). Based on the detailed analysis on the research development of IoT-related multimedia security and privacy protection, we point out some open challenges and provide future research directions, aiming to advance the study in the relevant fields and assist researchers in gaining a deeper understanding of the state of the art on multimedia data protection in the IoT.