Chronic kidney disease (CKD) is characterised by poor physical function. Mechanical muscle properties such as tone, elasticity, and stiffness influence the functional state of the muscle. Measuring these muscle mechanical properties is difficult and data on CKD are sparse. Using a novel myotonometer device, the aims of this study were to compare the viscoelastic muscle properties in CKD patients with previously reported data and to explore the association with muscle function. Non-dialysis-dependent CKD participants were recruited into a cross-sectional study conducted between 2018 and 2020. Muscle properties (tone, stiffness, elasticity) were assessed using a myotonometer (MyotonPRO). Muscle function was assessed using physical performance tests (sit-to-stand 5 and 60, timed up and go, short physical performance battery, gait speed, incremental shuttle walk, postural sway). General linear regression models were used to explore the association between muscle properties and physical function. Thirty-nine participants were included (age 64.2 (SD: 10.4) years; 51% male; eGFR 40.9 (SD: 20.0) mL/min/1.73 m2). Participants with CKD had reduced muscle tone, stiffness, and elasticity compared to previously reported studies. Muscle tone (B = −0.567, p = 0.003) and muscle stiffness (B = −0.368, p = 0.071) were greater in males than females. Increased BMI was associated with lower muscle tone (B = −0.528, p = 0.002) and muscle stiffness (B = −0.577, p = 0.002). No meaningful nor consistent associations were found between these properties and measures of muscle function and physical performance. In conclusion, using a novel handheld myotonometer, this study found that CKD patients exhibit a reduction in muscle tone, stiffness, and elasticity. In a passive state, these viscoelastic muscle properties showed no consistent associations with physical performance.