Massive multiple input multiple output (MIMO) is one of the key technologies for fifth generation and can substantially improve energy and spectrum efficiencies. This paper explores the potential benefits of massive MIMO in spectrum sharing networks. We consider a multiuser MIMO primary network, with Np-antenna primary base station (PBS) and K single-antenna primary users (PUs), and a multiple-input-single-output secondary network, with Ns-antenna secondary base station and a single-antenna secondary user. Using the proposed model, we derive a tight closed-form expression for the lower bound on the average achievable rate, which is applicable to arbitrary system parameters. By performing large-system analysis, we examine the impact of large number of PBS antennas and large number of PUs on the secondary network. It is shown that, when Np and K grow large, Ns must be proportional to ln K or larger, to enable successful secondary transmission. In addition, we examine the impact of imperfect channel state information on the secondary network. It is shown that the detrimental effect of channel estimation errors is significantly mitigated as Ns grows large.