Context. The Small Magellanic Cloud (SMC) is hosting many known high-mass X-ray binaries, all but one (SMC X-1) having Be companion stars. Through the calibration and verification phase of eROSITA on board the SRG spacecraft, the Be/X-ray binary XMMU J010429.4-723136 was in the field of view during observations of the supernova remnant 1E0102.2-7219, used as calibration standard. Aims. We report here a time and spectral analysis of XMMU J010429.4-723136, based on two eROSITA observations of the field, performed on 2019 November 7-9. We also reanalyse the OGLE light curve for that source, in order to determine the orbital period. Methods. The search for pulsations (from the X-ray data) and for the orbital period (from the OGLE data) is done via Lomb-Scargle periodogram analysis. X-ray spectral parameters and fluxes are retrieved from the best-fit model. Results. We detected for the first time, the pulsations of XMMU J010429.4-723136 at a period of 164 s, and therefore designate the source as SXP 164. From the spectral fitting, we derive a source flux of 1x10e-12 erg s-1 cm-2 for both observations, corresponding to a luminosity of 4x10e35 erg s-1 at the distance of the SMC. Furthermore, reanalysing the OGLE light curve including the latest observations, we found a significant periodic signal at 22.3d likely being the orbital period, which is shorter than the previously reported values.