We construct Absorbing Boundary Conditions (ABCs) for the convected Helmholtz equation. The construction is based upon the Prandtl-Glauert-Lorentz map which transforms the convected Helmholtz equation into the regular Helmholtz equations. The new ABCs are thus issued from classical Engquist-Majda ABCs and are valid for carrier flows that vary inside the domain but become uniform at infinity. They lead to accurate numerical results for low and intermediate Mach numbers and are easy to implement in an existing finite element or discontinuous Galerkin solver.