Association between physical performance and movement quality remains ambiguous. However, both affect injury risk. Furthermore, existing research rarely regards women. Therefore, this study aimed to assess the impact of physical performance components on FMS scores and asymmetries among young women—University Physical Education Students. The study sample was 101 women, 21.72 ± 1.57 years, body mass index 21.52 ± 2.49 [kg/m2]. The FMS test was conducted to assess the movement patterns quality. Physical performance tests were done to evaluate strength, power, flexibility. Flexibility has the strongest correlation with FMS overall (r = 0.25, p = 0.0130) and single tasks scores. A higher level of flexibility and strength of abdominal muscles are associated with fewer asymmetries (r = −0.31, p = 0.0018; r = −0.27, p = 0.0057, respectively). However, the main findings determine that flexibility has the strongest and statistically significant impact on FMS overall (ß = 0.25, p = 0.0106) and asymmetries (ß = −0.30, p = 0.0014). Additionally, a significant effect of abdominal muscles strength on FMS asymmetries were observed (ß = −0.29, p = 0.0027). Flexibility and abdominal muscles strength have the most decisive impact on movement patterns quality. These results suggest possibilities for shaping FMS scores in young women.