The interplay between topology and magnetism offers new opportunity for realizing exotic quantum phenomena. MnBi₂Te₄ (MBT) exhibits novel intrinsic magnetic topological properties, including the quantum anomalous Hall effect and the axion insulator state. As a two-dimensional van der Waals antiferromagnetic material, MBT can be exfoliated into atomically thin flakes, which enables studies of layer-number-dependent magnetism. Here, we present results of Raman spectroscopy experiments on 1- to 5-septuple-layer-thick MBT flakes, which provide significant new insights into interlayer coupling, spin collective motion, and ordering. In the low-frequency regime, we observed strong interlayer phonon peaks coming from substantial interfacial coupling. In addition, we observed another rising peak with magnonic feature below the Néel temperature in the presence of an external magnetic field. These results provide new systematic information on the layer-number-dependent spin and phonon properties of this topological magnetic material