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The atomically thin MnBi₂Te₄ crystal is a novel magnetic topological insulator, exhibiting exotic quantum physics. Here we report a systematic investigation of ultrafast carrier dynamics and coherent interlayer phonons in few-layer MnBi₂Te₄ as a function of layer number using time-resolved pump-probe reflectivity spectroscopy. Pronounced coherent phonon oscillations from the interlayer breathing mode are directly observed in the time domain. We find that the coherent oscillation frequency, the photocarrier and coherent phonon decay rates all depend sensitively on the sample thickness. The time-resolved measurements are complemented by ultralow-frequency Raman spectroscopy measurements, which both confirm the interlayer breathing mode and additionally enable observation of the interlayer shear mode. The layer dependence of these modes allows us to extract both the out-of-plane and in-plane interlayer force constants. Our studies not only reveal the interlayer van der Waals coupling strengths, but also shed light on the ultrafast optical properties of this novel two-dimensional material.