We study dephasing in an electronic Mach-Zehnder (MZ) interferometer based on quantum Hall edge states by a micrometer-sized Ohmic contact embedded in one of its arms. We find that at the filling factor ν=1, as well as in the case where an Ohmic contact is connected to a MZ interferometer by a quantum point contact that transmits only one electron channel, the phase coherence may not be fully suppressed. Namely, if the voltage bias Δμ and the temperature T are small compared to the charging energy of the Ohmic contact E_{C}, the free fermion picture is manifested, and the visibility saturates at its maximum value. At large biases, Δμ≫E_{C}, the visibility decays in a power-law manner.