We propose to operate massive multiple-input multiple output (MIMO) cellular base stations (BSs) in unlicensed bands. We denote such system as massive MIMO unlicensed (mMIMO-U). We design the key procedures required at a cellular BS to guarantee coexistence with nearby Wi-Fi devices operating in the same band. In particular, spatial reuse is enhanced by actively suppressing interference towards neighboring Wi-Fi devices. Wi-Fi interference rejection is also performed during an enhanced listen-before-talk (LBT) phase. These operations enable Wi-Fi devices to access the channel as though no cellular BSs were transmitting, and vice versa. Under concurrent Wi-Fi and BS transmissions, the downlink rates attainable by cellular user equipment (UEs) are degraded by the Wi-Fi-generated interference. To mitigate this effect, we select a suitable set of UEs to be served in the unlicensed band accounting for a measure of the Wi-Fi/UE proximity. Our results show that the so-designed mMIMO-U allows simultaneous cellular and Wi-Fi transmissions by keeping their mutual interference below the regulatory threshold. Compared to a system without interference suppression, Wi-Fi devices enjoy a median interference power reduction of between 3 dB with 16 antennas and 18 dB with 128 antennas. With mMIMO-U, cellular BSs can also achieve large data rates without significantly degrading the performance of Wi-Fi networks deployed within their coverage area.