Three types of shallow flows are widespread in nature and engineering: wakes, mixing layers and jets. Linear stability analysis of shallow wake flows is performed in [1], where weakly nonlinear evolution equation (the complex Ginzburg-Landau equation) for the most unstable mode is derived. Results of linear and nonlinear modeling of shallow wakes are presented in [2]. In the present paper we analyze the effect of small curvature on the linear and weakly nonlinear instability of shallow mixing layers. Linear stability analysis is performed under the rigid-lid assumption. It is shown that the linear stability equation is the modified Rayleigh equation. The problem is solved numerically by means of a collocation method based on Chebyshev polynomials. Results of numerical calculations show that curvature has stabilizing effect on a stably curved mixing layer and destabilizes the flow for the case of an unstably curved mixing layer. Method of multiple scales is used to derive an amplitude evolution equation for the most unstable mode if the bed-friction number is slightly smaller than the critical value. The coefficients of the amplitude equation (the complex Ginzburg-Landau equation) are calculated in closed form and are expressed in terms of the linear stability characteristics of the flow.