We report on the detection of the millisecond pulsar PSR J0437-4715 with the Murchison Widefield Array (MWA) at a frequency of 192 MHz. Our observations show rapid modulations of pulse intensity in time and frequency that arise from diffractive scintillation effects in the interstellar medium (ISM), as well as prominent drifts of intensity maxima in the time-frequency plane that arise from refractive effects. Our analysis suggests that the scattering screen is located at a distance of $sim$80-120 pc from the Sun, in disagreement with a recent claim that the screen is closer ($sim$10 pc). Comparisons with higher frequency data from Parkes reveals a dramatic evolution of the pulse profile with frequency, with the outer conal emission becoming comparable in strength to that from the core and inner conal regions. As well as demonstrating high time resolution science capabilities currently possible with the MWA, our observations underscore the potential to conduct low-frequency investigations of timing-array millisecond pulsars, which may lead to increased sensitivity for the detection of nanoHertz gravitational waves via the accurate characterisation of ISM effects.