Transcranial direct current stimulation (tDCS) over the primary motor cortex (M1) is of increasing interest to improve motor performance in healthy adults and patients with respective deficits. This study aimed to examine whether tDCS over M1 can improve static and dynamic postural stability in young healthy adults. Seventeen healthy participants (mean age = 25.14 ± 2.50 (standard deviation, SD) years) received sham and anodal tDCS (2 mA) over the vertex at the Cz electrode position for 15 min. Static and dynamic postural stability were evaluated before and immediately after tDCS. The center of pressure (COP) sway area (COP) and COP maximum displacements to medio-lateral (COP) and antero-posterior directions (COP) were used to evaluate static postural stability. The anterior–posterior stability index (APSI), medial–lateral stability index (MLSI), vertical stability index (VSI), dynamic postural stability index (DPSI), and time to stabilization (TTS) in forward (FL), 45° anterior lateral (LL), and 45° anterior medial (ML) direction landing, as well as the Y-balance composite score (YBT) were used to assess dynamic postural stability. The results showed that the LL-TTS (p = 0.044), non-dominant leg COP (p = 0.015), and YBT (p < 0.0001) were significantly improved in the real stimulation as compared with the sham stimulation session, and anodal tDCS significantly changed dominant leg COP (p = 0.021), FL-APSI (p < 0.0001), FL-TTS (p = 0.008), ML-TTS (p = 0.002), non-dominant leg YBT (p < 0.0001), and dominant leg YBT (p = 0.014). There were no significant differences in all obtained balance values in the sham stimulation session, except for non-dominant leg YBT (p = 0.049). We conclude that anodal tDCS over M1 has an immediate improving effect on static postural stability and dynamic performance in young healthy adults. This makes tDCS a promising adjuvant rehabilitation treatment to enhance postural stability deficits in the future.