We report the discovery of a low mass-ratio planet $(q = 1.3times10^{-4})$, i.e., 2.5 times higher than the Neptune/Sun ratio. The planetary system was discovered from the analysis of the KMT-2017-BLG-0165 microlensing event, which has an obvious short-term deviation from the underlying light curve produced by the host of the planet. Although the fit improvement with the microlens parallax effect is relatively low, one component of the parallax vector is strongly constrained from the light curve, making it possible to narrow down the uncertainties of the lens physical properties. A Bayesian analysis yields that the planet has a super-Neptune mass $(M_{2}=34_{-12}^{+15}~M_{oplus})$ orbiting a Sun-like star $(M_{1}=0.76_{-0.27}^{+0.34}~M_{odot})$ located at $4.5~{rm kpc}$. The blended light is consistent with these host properties. The projected planet-host separation is $a_{bot}={3.45_{-0.95}^{+0.98}}~{rm AU}$, implying that the planet is located outside the snowline of the host, i.e., $a_{sl}sim2.1~{rm AU}$. KMT-2017-BLG-0165Lb is the sixteenth microlensing planet with mass ratio $q<3times10^{-4}$. Using the fifteen of these planets with unambiguous mass-ratio measurements, we apply a likelihood analysis to investigate the form of the mass-ratio function in this regime. If we adopt a broken power law for the form of this function, then the break is at $q_{rm br}simeq0.55times10^{-4}$, which is much lower than previously estimated. Moreover, the change of the power law slope, $zeta>3.3$ is quite severe. Alternatively, the distribution is also suggestive of a pile-up of planets at Neptune-like mass ratios, below which there is a dramatic drop in frequency.
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