This study presents a warping included mixed finite element formulation for the static and stress analyses of functionally graded (FG) exact curved beams. Another distinctive feature of this study is to present the range of geometric and material parameters where the first-order shear deformation theory lacks necessary precision. The constitutive equations are derived from the 3D elasticity theory of an elastic continuum. The couple effects are considered in addition to the variations of FG material constituents through the transverse/axial directions. The mixed finite element formulation is enhanced by the cross-sectional warping deformations over a displacement-type finite element formulation. The two-noded curved mixed finite elements with 12 degrees of freedom at per node are derived over exact curvature and length. Satisfactory results are obtained for the static responses and stresses of axially FG-sandwich and transversely FG exact curved beams with power-law dependence compared to the 3D behavior of brick finite elements. Finally, the influences of ellipticity, width to thickness ratio, FG material constituents, and material gradient index on the static response of FG exact curved beams are investigated.