We studied single-sideband (SSB) photonic microwave generation with a high sideband rejection ratio (SRR) based on the period-one dynamical states of an optically injected quantum-dot (QD) semiconductor laser and demonstrated that the SSB signals have SRRs of approximately 15 dB higher than those generated with a conventional quantum-well semiconductor laser under conditions of optimal microwave power. The enhancement of SRR in the QD laser, which is important in mitigating the power penalty effect in applications such as radio-over-fiber optical communications, could be primarily attributed to a lower carrier decay rate in the dots, smaller linewidth enhancement factor, and reduced photon decay rate.