We report on our observing campaign of the compact binary merger GW190814, detected by the Advanced LIGO and Advanced Virgo detectors on 2019 August 14. This signal has the best localization of any observed gravitational wave (GW) source, with a 90 per cent probability area of 18.5 deg2, and an estimated distance of ≍240 Mpc. We obtained wide-field observations with the Deca-Degree Optical Transient Imager (DDOTI) covering 88 per cent of the probability area down to a limiting magnitude of w = 19.9 AB. Nearby galaxies within the high probability region were targeted with the Lowell Discovery Telescope (LDT), whereas promising candidate counterparts were characterized through multicolour photometry with the Reionization and Transients InfraRed (RATIR) and spectroscopy with the Gran Telescopio de Canarias (GTC). We use our optical and near-infrared limits in conjunction with the upper limits obtained by the community to constrain the possible electromagnetic counterparts associated with the merger. A gamma-ray burst seen along its jet's axis is disfavoured by the multiwavelength data set, whereas the presence of a burst seen at larger viewing angles is not well constrained. Although our observations are not sensitive to a kilonova similar to AT2017gfo, we can rule out high-mass (>0.1 M☉) fast-moving (mean velocity ≥0.3c) wind ejecta for a possible kilonova associated with this merger.