MnBi₂Te₄ represents a new class of magnetic topological insulators in which novel quantum phases emerge at temperatures higher than those found in magnetically doped thin films. Here, we investigate how couplings between electron, spin, and lattice are manifested in the phonon spectra of few-septuple-layer thick MnBi₂Te₄. After categorizing phonon modes by their symmetries, we study the systematic changes in frequency, line width, and line shape of a spectrally isolated A_1g mode. The electron–phonon coupling increases in thinner flakes as manifested in a broader phonon line width, which is likely due to changes of the electron density of states. In 4- and 5-septuple thick samples, the onset of magnetic order below the Néel temperature is concurrent with a transition to an insulating state. We observe signatures of a reduced electron–phonon scattering across this transition as reflected in the reduced Fano parameter. Finally, spin–lattice coupling is measured and modeled from temperature-dependent phonon frequency.