In everyday life, we recurrently perform two tasks simultaneously, which is called dual-tasking. A common dual task is smartphone use while standing or walking. According to previous studies, this task can compromise postural stability. However, few studies have analyzed lower limb muscle activity during dual-tasking using smartphones. This study aimed to assess the postural sway and muscle activity during dual-tasking in young adults. Thirty-six healthy young adults (23.08 ± 3.92 years) participated in this study. They performed a single task (ST: keeping a quiet standing posture) and a dual task (DT: keeping the ST while simultaneously performing a cognitive task on their smartphone). Postural sway was assessed through the center of pressure (CoP) analysis using a force platform: total CoP displacement, CoP displacement in the anterior–posterior and medial–lateral directions, mean total velocity of the CoP, mean velocity of the CoP in the anterior–posterior and medial–lateral directions, and 95% confidence ellipse sway area. A surface electromyography system recorded the muscle activity of the lumbar spinal erector and five muscles of the lower limb (bilaterally). The results showed an increase in postural sway from the ST to the DT in all CoP variables (p < 0.05), and muscle activity in most muscles analyzed decreased from the ST to the DT (p < 0.05). In conclusion, our results reflect a decentralization of attention from motor performance once postural sway increased and muscle activity decreased in dual-task conditions.