The applications of industrial polymers have grown extensively owing to the fact of their competent performance characteristics, at par with commonly used engineering materials, as well as technological breakthroughs. Friction stir welding (FSW) of thermoplastics is a recent approach that enabled the permanent joining of similar or dissimilar polymers with desirable efficacy. The primary purpose of the present study is to investigate the effect of friction stir welding process parameters on the welding characteristics (tensile and flexural strength) of the two dissimilar thermoplastics, high-density polythene and polyamide (PA-6). Processing parameters such as the number of passes, pre-heating temperature, tool speed, feed rate, and plunge-in-time have been selected as input parameters, and their influence on the above-mentioned mechanical properties has been studied through Taguchi L-18-based design of experimentation. Further, the morphological investigations of the weld interface and the fractured joint have been studied by using scanning electron microscopy. It has been found that the tool speed has contributed 27.88% and 58.46% in tensile and flexural strength, respectively, at 95% confidence level. Overall, it has been found that the process parameters of FSW have a strong influence on the joint’s characteristics and shown importance to study for the futuristic developments in this technology.