Several studies have documented periodic and quasi-periodic signals from the time series of dMe flare stars and other stellar sources. Such periodic signals, observed within quiescent phases (i.e., devoid of larger-scale microflare or flare activity), range in a period from 1 to 1000 s and hence have been tentatively linked to ubiquitous p-mode oscillations generated in the convective layers of the star. As such, most interpretations for the observed periodicities have been framed in terms of magnetohydrodynamic wave behavior. However, we propose that a series of continuous nanoflares, based upon a power-law distribution, can provide a similar periodic signal in the associated time series. Adapting previous statistical analyses of solar nanoflare signals, we find the first statistical evidence for stellar nanoflare signals embedded within the noise envelope of M-type stellar lightcurves. Employing data collected by the Next Generation Transit Survey (NGTS), we find evidence for stellar nanoflare activity demonstrating a flaring power-law index of 3.25 ± 0.20, alongside a decay timescale of 200 ± 100 s. We also find that synthetic time series, consistent with the observations of dMe flare star lightcurves, are capable of producing quasi-periodic signals in the same frequency range as p-mode signals, despite being purely composed of impulsive signatures. Phenomena traditionally considered a consequence of wave behavior may be described by a number of high-frequency but discrete nanoflare energy events. This new physical interpretation presents a novel diagnostic capability, by linking observed periodic signals to given nanoflare model conditions.