We demonstrate wavelength conversion based on four-wave mixing in a semiconductor optical amplifier of signals with quadrature amplitude modulation (QAM). We first demonstrate wavelength conversion of 16 Gbaud 16-QAM signals over the entire C-band using two co-polarized pumps with low power penalty at the forward error correction threshold (FEC) for a wide range of input optical-signal-to-noise-ratio (OSNR). We also demonstrate for the first time wavelength conversion of 5 Gbaud 64-QAM signals in a semiconductor optical amplifier with bit-error rate below the FEC threshold over the entire C-band and investigate the dependence of the power penalty on input OSNR with a single pump configuration.