A functional linear autoregressive spatial model, where the explanatory variable takes values in a function space, while the response process is real-valued and spatially autocorrelated, is proposed. The specificity of the model is due to the functional nature of the explanatory variable and the structure of a spatial weight matrix that defines the spatial dependency between neighbors. The estimation procedure consists of reducing the infinite dimension of the functional explanatory variable and maximizing the quasi-maximum likelihood. We establish the consistency and asymptotic normality of the estimator. The ability of the methodology is illustrated via simulations and by application to real data.