The Advanced LIGO and Virgo gravitational wave observatories detected a signal on 2019 August 14 during their third observing run, named GW190814. A large number of electromagnetic facilities conducted follow-up campaigns in the search for a possible counterpart to the gravitational wave event, which was made especially promising given the early source classification of a neutron star-black hole merger. We present the results of the GW follow-up campaign taken with the wide-field optical telescope MeerLICHT, located at the South African Astronomical Observatory Sutherland site. We use our results to constrain possible kilonova models. MeerLICHT observed more than 95% of the probability localisation each night for over a week in three optical bands (u,q,i) with our initial observations beginning almost 2 hours after the GW detection. We describe the search for new transients in MeerLICHT data and investigate how our limiting magnitudes can be used to constrain an AT2017gfo-like kilonova. A single new transient was found in our analysis of MeerLICHT data, which we exclude from being the electromagnetic counterpart to GW190814 owing to the existence of a spatially unresolved source at the coordinates of the transient in archival data. Using our limiting magnitudes, the confidence with which we can exclude the presence of an AT2017gfo-like kilonova at the distance of GW190814 was low (<10^-4^).