Irrigation canals are large-scale systems, covering vast geographical areas, and consisting of many interconnected canal reaches that interact with control structures such as pumps and gates. The control of such irrigation canals is usually done in a manual way, in which a human operator travels along the irrigation canal to adjust the settings of the gates and pumps in order to obtain a desired water level. In this paper we discuss how distributed model predictive control (MPC) can be applied to determine autonomously what the settings of these control structures should be. In particular, we propose the application of a distributed MPC scheme for control of the West-M irrigation canal in Arizona. We present a linearized model representing the dynamics of the canal, we propose a distributed MPC scheme that uses this model as a prediction model, and we illustrate the performance of the scheme in simulation studies on a nonlinear simulation model of the canal.