The low-noise operation of readout electronics in a liquid argon time projection chamber (LArTPC) is critical to properly extract the distribution of ionization charge deposited on the wire planes of the TPC, especially for the induction planes. This paper describes the characteristics and mitigation of the observed noise in the MicroBooNE detector. The MicroBooNE's single-phase LArTPC comprises two induction planes and one collection sense wire plane with a total of 8256 wires. Current induced on each TPC wire is amplified and shaped by custom low-power, low-noise ASICs immersed in the liquid argon. The digitization of the signal waveform occurs outside the cryostat. Using data from the first year of MicroBooNE operations, several excess noise sources in the TPC were identified and mitigated. The residual equivalent noise charge (ENC) after noise filtering varies with wire length and is found to be below 400 electrons for the longest wires (4.7 m). The response is consistent with the cold electronics design expectations and is found to be stable with time and uniform over the functioning channels. This noise level is significantly lower than previous experiments utilizing warm front-end electronics.