This paper considers the uplink performance of a multi-user massive multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) system with mobile users. Mobility brings two major problems to a MIMO-OFDM system: inter carrier interference (ICI) and channel aging. In practice, it is common to allot multiple contiguous subcarriers to a user as well as schedule multiple users on each subcarrier. Motivated by this, we consider a general subcarrier allocation scheme and derive expressions for the ICI power, uplink signal to interference plus noise ratio and the achievable uplink sum-rate, taking into account the ICI and the multi-user interference due to channel aging. We show that the system incurs a near-constant ICI power that depends linearly on the ratio of the number of users per subcarrier to the number of subcarriers per user, nearly independently of how the UEs distribute their power across the subcarriers. Further, we exploit the coherence bandwidth of the channel to reduce the length of the pilot sequences required for uplink channel estimation. We consider both zero-forcing and maximal-ratio combining at the receiver and compare the respective sum-rate performances. In either case, the proposed subcarrier allocation scheme leads to significantly higher sum-rates compared to previous work, owing to the near-constant ICI property as well as the reduced pilot overhead.