We have searched for microsecond bursts of emission from millisecond pulsars in the globular cluster M28 using the Parkes radio telescope. We detected a total of 27 giant pulses from the known emitter PSR J1824-2452A. At wavelengths around 20 cm the giant pulses are scatter broadened to widths of around 2 µs and follow power-law statistics. The pulses occur in two narrow phase windows that correlate in phase with X-ray emission and trail the peaks of the integrated radio pulse components. Notably, the integrated radio emission at these phase windows has a steeper spectral index than other emission. The giant pulses exhibit a high degree of polarization, with many being 100% elliptically polarized. Their position angles appear random. Although the integrated emission of PSR J1824-2452A is relatively stable for the frequencies and bandwidths observed, the intensities of individual giant pulses vary considerably across our bands. Two pulses were detected at both 2700 and 3500 MHz. The narr6Fwer of the two pulses is 20 ns wide at 3500 MHz. At 2700 MHz this pulse has an inferred brightness temperature at maximum of 5 x 10/37 K. Our observations suggest the giant pulses of PSR J1824-2452A are generated in the same part of the magnetosphere as X-ray emission through a different emission process to that of ordinary pulses.