Osteoarthritis (OA) is a chronic and progressive joint disease, leading to functional limitations and significantly impairing the quality of life. Muscle weakness, reduced mobility, and compensatory biomechanical changes are common consequences, further exacerbating functional decline. The aim of this study was to assess the impact of hip osteoarthritis on muscle functionality and to evaluate the effectiveness of hip arthroplasty using the MyotonPro device to measure key biomechanical parameters, i.e., tension, stiffness, and flexibility. Methods: This cohort study included 40 patients (17 women and 23 men; mean age 64.55 ± 10.49 years) with advanced hip OA (Kellgren–Lawrence grade III–IV) undergoing hip arthroplasty. Measurements of muscle tension (F), stiffness (S), and flexibility (D) in the gluteus maximus, rectus femoris, and biceps femoris were performed at three time points: before surgery, on postoperative days 8–10, and one month after hospital discharge. Pain (VAS), balance (Tinetti scale), and functional ability (WOMAC index) were also assessed. Results: Hip arthroplasty significantly reduced pain levels (VAS: 6.38 ± 0.28 preoperatively to 1.88 ± 0.22 postoperatively, p < 0.001) and improved functional ability (WOMAC: p < 0.001). Muscle tension and stiffness of the gluteus maximus initially increased after surgery (tension: 11.57 ± 0.32 to 12.15 ± 0.38, p = 0.009), reflecting compensatory stabilization but decreased by the final evaluation. Flexibility improved significantly over time (p = 0.014). The biceps femoris muscle exhibited a significant reduction in tension one month postoperatively (p = 0.015), alongside decreased stiffness (p = 0.015) and enhanced flexibility. The rectus femoris muscle showed minor changes in biomechanical properties, with no statistically significant differences detected. Conclusions: Osteoarthritis significantly impacts muscle function, reducing the gluteus muscle tension and stiffness, which compromises joint stability and triggers compensatory activity in the rectus femoris and biceps femoris muscles. Postoperative rehabilitation is essential for improving flexibility and addressing compensatory muscle tension.