Partially linear spatial autoregressive model has attracted extensive attention in recent years because it combines explanatory power of parametric spatial autoregressive models and flexibility of nonparametric spatial autoregressive model. This paper considers the problem of variable selection in the partially linear spatial autoregressive model. Based on profile quasi-maximum likelihood method and a class of non-convex penalty function, a class of penalized least squares method is proposed to simultaneously select significant explanatory variables in parametric component of the model and estimate corresponding nonzero regression coefficients. Under appropriate regularity conditions, the rate of convergence of the penalized estimator of the regression coefficient vector is derived and it shows that the proposed variable selection method enjoys oracle property. Both simulation studies and real data analysis indicate that the proposed variable selection method has satisfactory finite sample performance.