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Internet of Things (IoT) ideates smart and inter-connected things capable of sharing their perceptions through the Internet. These devices are different from conventional Internetconnected devices in the sense that these are able to perform skill-full things on their own with minimal or no human interaction. Unfortunately, with the advent of amalgamate technologies, security has become a major concern for IoT networks. Recent efforts include re-inventing cryptographic solutions through the use of light-weight operations. However, after witnessing the growth of quantum computers, it can be inferred that the cryptographic techniques based on mathematical problems are not reliable enough. Therefore, there is need to develop solutions that can easily resist the adversarial effects and are suitable for the post-quantum world. In this paper, we perform in-depth analysis over the role of post-quantum cryptographic techniques for securing IoT networks and also explore ongoing research efforts in the field. In addition, we discuss the open research challenges and future research directions in the field.