In this article, we are interested in the behavior of discontinuous Galerkin schemes for compressible flows in the low Mach number limit. We prove that for any numerical flux conserving exactly contacts (e.g., exact Godunov, Roe, HLLC), the numerical scheme is accurate at low Mach number flows on simplicial meshes, which is an extension to higher order of the result proven in [H. Guillard, Comput. Fluids, 38 (2009), pp. 1969--1972]. When the mesh is not simplicial, or when the mesh is simplicial but the numerical flux does not conserve contacts (e.g., Lax-Friedrich, HLL), the scheme is numerically proven to be less accurate in the low Mach number limit.