Walking requires attentional resources, and the studies using neuroimage techniques have grown to understand the interaction between cortical activity and motor performance. Previous studies reported a decline in gait performance and changes in the prefrontal cortex (PFC) activity during a dual-task performance compared to walking only. Some lifestyle factors, such as sleep and physical activity (PA) levels, can compromise walking performance and brain activity. Nonetheless, the studies are scarce. This study aimed to assess gait speed and hemodynamic response in the PFC during a cognitive dual-task (cog-DT) compared to walking only, and to analyze the correlation between PA and sleep quality (SQ) with gait performance and hemodynamic response in the PFC during a single task (ST) and cog-DT performance in young adults. A total of 18 healthy young adults (mean age ± SD = 24.11 ± 4.11 years) participated in this study. They performed a single motor task (mot-ST)—normal walking—and a cog-DT—walking while performing a cognitive task on a smartphone. Gait speed was collected using a motion capture system coupled with two force plates. The hemoglobin differences (Hb-diff), oxyhemoglobin ([oxy-Hb]) and deoxyhemoglobin ([deoxy-Hb]) concentrations in the PFC were obtained using functional near-infrared spectroscopy. The SQ and PA were assessed through the Pittsburg Sleep Quality Index and International Physical Activity Questionnaire-Short Form questionnaires, respectively. The results show a decrease in gait speed (p < 0.05), a decrease in [deoxy-Hb] (p < 0.05), and an increase in Hb-diff (p < 0.05) and [oxy-Hb] (p > 0.05) in the prefrontal cortex during the cog-DT compared to the single task. A positive correlation between SQ and Hb-diff during the cog-DT performance was found. In conclusion, the PFC’s hemodynamic response during the cog-DT suggests that young adults prioritize cognitive tasks over motor performance. SQ only correlates with the Hb-diff during the cog-DT, showing that poor sleep quality was associated with increased Hb-diff in the PFC. The gait performance and hemodynamic response do not correlate with physical activity level.