The current practice of implementing tornadic wind actions on structures in building codes is not well established compared to atmospheric boundary layer winds. Given there is a lack of velocity measurements in actual tornados close to the surface, there is a body of research that is currently looking into physical simulations of tornado-like vortices (TLVs). Our study contributes to this field of research by looking into the aerodynamic effects a generic building exerts on TLVs that are stationary and positioned above the building. Our study also investigated the differences among two distinctively different velocity measurement techniques in TLV flows—Cobra probe and particle image velocimetry (PIV). We further examine how different TLV intensities affect the results by considering TLVs that correspond to (Enhanced Fujita) EF1- and EF2-rated tornadoes in the atmosphere. We show that the velocity fluctuations in Cobra probe records are higher than in PIV measurements despite both velocity records being sampled at 200 Hz. The discrepancy is due to the inherent spatial filtering used in PIV data processing. A larger discrepancy between the two measurement techniques was observed in the EF1 TLV. The presence of the building affected EF1 more than EF2 TLV due to the larger core diameter of the latter vortex. The diameter of the circumference of the maximum tangential velocity in EF1 and EF2 TLVs undisturbed by the building was 1.6 and 2.1 times larger than the diagonal length of the building. By comparing our results against prior research on the same TLVs, but without a building in the flow, we concluded that the building had the strongest effect in amplifying vertical velocity in the EF2 TLV. The significance of this result to wind loading and structural responses requires further wind engineering analyses. The circular symmetry of EF1 was more affected than in EF2 TLV due to its smaller size relative to the building.