The aim of this study was to assess the effects of a six-week core stability training program on the fundamental movement pattern assessed using the Functional Movement Screen Test in tennis players. The study group consisted of 160 subjects (74 women, 86 men) with a mean age of 20.26 ± 1.55. The Functional Movement Screen Test (FMS™), as well as the core stability tests including the lateral trunk muscles endurance test (the side bridge test), the abdominal muscles endurance test and the trunk extensors muscle endurance test—were used to evaluate the effects of core stability training. Statistical analysis revealed significant differences in the FMS test scores before and after introducing a core stability exercise program. Initially, the average total score of the FMS test in female tennis players was 14.58 ± 2.91, and after core stability training it was 17.20 ± 1.68 (p < 0.001). In the male group, the total FMS test score was 14.44 ± 2.76 before and 16.91 ± 1.36 after (p < 0.001) in the final assessment. Additionally, statistically significant differences were observed in the core stability test scores before and after introducing a stabilisation training program. The results of the study showed that specific core strengthening exercises could improve the FMS test scores in adult tennis players. This may also have an influence on reducing injury risk in this group, although further studies would be required to test this.