On 18 November 2022, a strong earthquake occurred in the near-trench of Sunda Arc southwest of southern Sumatra, generating a small tsunami recorded at four tide gauge stations (KRUI, BINT, SBLT, and SIKA). Four seismological agencies (BMKG, GCMT, GFZ, and USGS) obtained nearly similar earthquake parameters and focal mechanisms from a seismic approach. It is situated near two major historical earthquakes that generated destructive tsunamis. One of those historical tsunamis, the 2010 Mentawai tsunami, was produced by a rare shallow and slow rupture earthquake with a higher tsunami impact than predicted from the seismic moment. It is related to the low rock rigidity of the source location. This study aims to understand the source characteristics of the 2022 event, which were probably influenced by the depth-varying rigidity. We examined those four source models using numerical tsunami modeling. We tested five distinct rigidity values, such as 10, 12.5, 15, 17.5, and 20 GPa, for each source model to obtain the best match of simulated and observed tsunami waveform. Waveform correlation coefficient and NRMSE are used as similarity indicators. The Mw 6.7 shallow source model with low rigidity (10 GPa) is the best model, as indicated by the correlation of ~0.74 and the lowest NRMSE. This solution is consistent with the long duration of the source time function of this event issued by IPGP. It is necessary to consider the appropriate rigidity characteristic in the tsunami hazard assessment since improper rigidity strongly affects the tsunami impact prediction in the coastal area.