This paper has two objectives: we first generalize the theory of Abhyankar–Moh to quasi-ordinary polynomials, then we use the notion of approximate roots and that of generalized Newton polygons in order to prove the embedding conjecture for this class of polynomials. This conjecture – made by S.S. Abhyankar and A. Sathaye – says that if a hypersurface of the affine space is isomorphic to a coordinate, then it is equivalent to it.