In this paper, we have focused on the Self-Determination Theory, paying special attention to intrinsic motivation, which is understood as the motivation that leads the subject to perform a task without the expectation of obtaining an external reward. In the field of sport, motivation is one of the most studied variables and one of the most researched, since it is closely related to the reasons that lead the athletes to start, maintain, and abandon sports practice. The main objective of this study is to analyze the relationship between intrinsic motivation (IM) and emotional intelligence from the theoretical contributions of the Self-Determination Theory. The specific objectives are to analyze attention, clarity, and emotional regulation, as well as intrinsic motivation to acquire knowledge. Additionally, we aim to explore the relationship between attention, clarity, and emotional regulation and the intrinsic motivation to achieve something. Lastly, we investigate the correspondence between attention, clarity, and emotional regulation and the intrinsic motivation to experience stimuli. The sample consists of 163 undergraduate and master’s students related to Physical Activity and Sports Sciences, studying at a Spanish public university, located in the southeast region of Andalusia—specifically, in the city of Almería. The participants had a mean age of 20.33 years. In terms of gender, 70.9% (n = 117) were men and 27.9% (n = 46) women. In terms of degree, 76.7% (n = 147) were undergraduate students and 23.3% (n = 18) were postgraduate students. The Sports Motivation Scale (SMS/EMD) was used to assess intrinsic motivation, and the TMMS-24 was used to assess emotional intelligence. The main findings of this research demonstrate the existence of a relationship between the three dimensions of emotional intelligence (emotional attention, emotional clarity, and emotional regulation) and intrinsic motivation (intrinsic motivation to know something, intrinsic motivation to achieve something, and intrinsic motivation to experience stimulation). These findings emphasize the importance of emotional intelligence for intrinsic motivation.