Understanding the cortical activation and postural control behavior during dual-task (DT) has been an object of study. However, despite the multiple benefits of exercise and good sleep quality, less is known about the correlation between physical activity (PA) and sleep quality (SQ) on postural control and brain activation under dual-task performance. This study aimed to analyze the correlation between PA level and SQ with postural control performance and hemodynamic response in the prefrontal cortex during the DT performance in young adults. Thirty-four healthy young adults (mean age ± SD = 22.91 ± 3.90 years) participated in this study, and they performed a single-task and cognitive and motor DT using their smartphones. Postural control was assessed using a force plate to record the center of pressure (CoP) data (total excursion of CoP (TOTEX CoP), displacements of the CoP in anterior-posterior (CoP-AP) and medial-lateral (CoP-ML) directions, mean total velocity displacement of CoP (MVELO CoP), mean displacement velocity of CoP in anterior-posterior (MVELO CoP-AP) and medial-lateral (MVELO CoP-ML) directions, amplitude of CoP in anterior-posterior (A-AP) and medial-lateral (A-ML) directions, and 95% confidence ellipse sway area (CEA)). The hemodynamic response was measured by the oxyhemoglobin and deoxyhemoglobin concentrations using the functional near-infrared spectroscopy. The Pittsburg Sleep Quality Index and International Physical Activity Questionnaire-Short Form questionnaires assessed SQ and level of PA, respectively. Results indicated a positive correlation between SQ and cognitive DT cost for CoP-ML (rs = 0.422, p = 0.013), MVELO CoP-ML (rs = 0.422, p = 0.013) and A-ML (rs = 0.579, p < 0.001). There were no significant relations between the other outcomes (p > 0.05). In conclusion, poor sleep quality was associated with a worse postural control performance in CoP-ML, MVELO CoP-ML and A-ML parameters under cognitive dual-task conditions. The differences found in the postural control and hemodynamic response during dual-task performance do not correlate with physical activity level.