Media-based modulation (MBM) is an attractive modulation scheme which is getting increased research attention recently. In this paper, we consider MBM for the uplink of a massive MIMO system, which has not been reported before. Each user is equipped with one transmit antenna with multiple radio frequency (RF) mirrors (parasitic elements) placed near it. The base station (BS) is equipped with tens to hundreds of receive antennas. We investigate the potential performance advantage of multiuser MBM (MU-MBM) in a massive MIMO setting. Our results show that multiuser MBM (MU-MBM) can significantly outperform other modulation schemes. For example, a bit error performance achieved using 500 receive antennas at the BS in a massive MIMO system using conventional modulation can be achieved using just 128 antennas using MU-MBM. Even multiuser spatial modulation and generalized spatial modulation in the same massive MIMO settings require more than 200 antennas to achieve the same bit error performance. Also, recognizing that the MU-MBM signal vectors are inherently sparse, we propose an efficient MU-MBM signal detection scheme that uses compressive sensing based reconstruction algorithms like orthogonal matching pursuit (OMP), compressive sampling matching pursuit (CoSaMP), and subspace pursuit (SP).