X-ray pulsations with a 6.85 s period were recently detected in the Small Magellanic Cloud (SMC) and were subsequently identified as originating from the Be/X-ray binary system XTE J0103-728. The recent localization of the source of the X-ray emission has made a targeted search for radio pulsations from this source possible. The detection of pulsed radio emission from XTE J0103-728 would make it only the second system after PSR B1259-63 that is both a Be/X-ray binary and a radio pulsar. We observed XTE J0103-728 in 2008 February with the Parkes 64 m radio telescope soon after the identification of the source of X-ray pulsations was reported in order to search for corresponding radio pulsations. We used a continuous 6.4 hr observation with a 256 MHz bandwidth centered at 1390 MHz using the center beam of the Parkes multibeam receiver. In the subsequent data analysis, which included a folding search, a Fourier search, a fast-folding algorithm search, and a single pulse search, no pulsed signals were found for trial dispersion measures (DMs) between 0 and 800 pc/cm3. This DM range easily encompasses the expected values for sources in the SMC. We place an upper limit of ∼45 mJy kpc2 on the luminosity of periodic radio emission from XTE J0103-728 at the epoch of our observation, and we compare this limit to a range of luminosities measured for PSR B1259-63, the only Be/X-ray binary currently known to emit radio pulses. We also compare our limit to the radio luminosities of neutron stars having similarly long spin periods to XTE J0103-728. Since the radio pulses from PSR B1259-63 are eclipsed and undetectable during the portion of the orbit near periastron, repeated additional radio search observations of XTE J0103-728 may be valuable if it is undergoing similar eclipsing and if such observations are able to sample the orbital phase of this system well.