Atomically thin two-dimensional molybdenum disulfide (MoS2) sheets have attracted much attention due to their potential for future electronic applications. They not only present the best planar electrostatic control in a device, but also lend themselves readily for dielectric engineering. In this work, we experimentally investigated the dielectric effect on the Raman and photoluminescence (PL) spectra of monolayer MoS2 by comparing samples with and without HfO2 on top by atomic layer deposition (ALD). Based on considerations of the thermal, doping, strain and dielectric screening influences, it is found that the red shift in the Raman spectrum largely stems from modulation doping of MoS2 by the ALD HfO2, and the red shift in the PL spectrum is most likely due to strain imparted on MoS2 by HfO2. Our work also suggests that due to the intricate dependence of band structure of monolayer MoS2 on strain, one must be cautious to interpret its Raman and PL spectroscopy.