This work theoretically investigates the relative intensity noise (RIN) and spectral linewidth characteristics of epitaxial quantum dot (QD) lasers on silicon subject to optical injection. The results show that the RIN of QD lasers can be reduced by optical injection, hence a reduction of 10 dB is achieved which leads to a RIN as low as -167.5 dB/Hz in the stable injection-locked area. Furthermore, the spectral linewidth of the QD laser can be greatly improved through the optical injection locked scheme. It is reduced from 556.5 kHz to 9 kHz with injection ratio of -60 dB and can be further reduced down to 1.5 Hz with injection ratio of 0 dB. This work provides an effective method for designing low intensity noise and ultra-narrow linewidth QD laser sources for photonics integrated circuits on silicon.