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Exciton-phonon interaction plays a major role in the relaxation dynamics of photocarriers in monolayer semiconducting transition metal dichalcogenides (TMDs). Despite a few experimental studies on phonon-limited excitonic relaxation, details behind which phonon modes and how they affect the formation and relaxation of excitons are still lacking. We observe an oscillatory enhancement of neutral exciton signal in monolayer MoSe₂ in photoluminescence excitation (PLE), with a period matching the M-point longitudinal acoustic phonon, LA(M). Numerical fit to the emission lineshapes also reveals the oscillatory behavior, suggesting that the presence of LA(M) phonons significantly modifies the relaxation dynamics. This is verified by our observation of oscillatory exciton lifetime in time-resolved PLE. What is unusual here is the dominating role of acoustic phonons, rather than optical phonons as commonly expected. Our theory suggests the importance of Q valleys in the dynamics of excitons, although photocarriers are predominantly localized in K valleys. Reference: Chow et al., npj 2D Mater. Appl. 1, 33 (2017).