In this work, the size-dependent effect for InGaN/GaN-based blue micro-light emitting diodes (µLEDs) is numerically investigated. Our results show that the external quantum efficiency (EQE) and the optical power density drop drastically as the device size decreases when sidewall defects are induced. The observations are owing to the higher surface-to-volume ratio for small µLEDs, which makes the Shockley-Read-Hall (SRH) non-radiative recombination at the sidewall defects not negligible. The sidewall defects also severely affect the injection capability for electrons and holes, such that the electrons and holes are captured by sidewall defects for the SRH recombination. Thus, the poor carrier injection shall be deemed as a challenge for achieving high-brightness µLEDs. Our studies also indicate that the sidewall defects form current leakage channels, and this is reflected by the current density-voltage characteristics. However, the improved current spreading effect can be obtained when the chip size decreases. The better current spreading effect takes account for the reduced forward voltage.