The mechanical properties of fibre-managed Eucalyptus nitens (E. nitens) cross-laminated timber (CLT) have previously been extensively studied, proving the material to be structurally safe and reliable. However, the vibration performance of CLT manufactured from this relative new construction species is not yet fully understood, especially under different support conditions. In this study, three types of support conditions, including roller–roller, bearer–bearer and clamp–bearer support conditions, were examined under vibration impulse-response testing performed using a simple but effective and repeatable excitation method consisting of a basketball dropped from a known height and an accelerometer. Six three-ply E. nitens CLT panels considered to have different moduli of elasticity in different layers and one strength-class C24 spruce CLT as a controlled reference were included in this study. The results suggest that the fundamental frequency values can effectively reflect the inherent characteristics of CLT panels (bending stiffness and density); however, no obvious relationship was observed between damping ratios and these inherent properties. The values of frequency constant λ1 were determined to analyse the effect of different support conditions on the values of fundamental frequency. The average values of λ1 for the roller–roller (9.6) and bearer–bearer (10.1) supports align with the theoretical values (9.87) for simply support (S-S) conditions. However, when clamping loads were applied at one edge of the bearer support, the average values of λ1 increased up to 10.8 but remained far below the theoretical values for clamped–pinned (C-S) support (15.4).