In this paper, we consider a downlink (DL) massive multiple-input multiple-output (MIMO) system, where different users have different mobility profiles. To support this system, we propose to use a hybrid orthogonal time frequency space (OTFS)/orthogonal frequency division multiplexing (OFDM) modulation scheme, where OTFS is applied for high-mobility users and OFDM is used for low-mobility users. Two precoding designs, namely full zero-forcing (FZF) precoding and partial zero-forcing (PZF) precoding, are considered and analyzed in terms of per-user spectral efficiency (SE). With FZF, interference among users is totally eliminated at the cost of high computational complexity, while PZF can be used to provide a trade-off between complexity and performance. To apply PZF precoding, users are grouped into two disjoint groups according to their mobility profile or channel gain. Then, zero-forcing (ZF) is utilized for high-mobility or strong channel gain users to completely cancel the inter-group interference, while maximum ratio transmission (MRT) is applied for low-mobility users or users with weak channel gain. To shed light on the system performance, the SE for high-mobility and low-mobility users with a minimum-mean-square-error (MMSE)-successive interference cancellation (SIC) detector is investigated. Our numerical results reveal that the PZF precoding with channel gain grouping can guarantee a similar quality of service for all users. In addition, with mobility-based grouping, the hybrid OTFS/OFDM modulation outperforms the conventional OFDM modulation for high-mobility users.