The friction stir welding (FSW) process was recently developed to overcome the difficulty of welding non-ferrous alloys and steels. In this study, dissimilar butt joints between 6061-T6 aluminum alloy and AISI 316 stainless steel were welded by FSW using different processing parameters. The grain structure and precipitates at the different welded zones of the various joints were intensively characterized by the electron backscattering diffraction technique (EBSD). Subsequently, the FSWed joints were tensile tested to examine the mechanical strength compared with that of the base metals. The micro-indentation hardness measurements were conducted to reveal the mechanical responses of the different zones in the joint. The EBSD results of the microstructural evolution showed that a significant continuous dynamic recrystallization (CDRX) occurred in the stir zone (SZ) of the Al side, which was mainly composed of the weak metal, Al, and fragmentations of the steel. However, the steel underwent severe deformation and discontinuous dynamic recrystallization (DDRX). The FSW rotation speed increased the ultimate tensile strength (UTS) from 126 MPa at a rotation speed of 300 RPM to 162 MPa at a rotation speed of 500 RPM. The tensile failure occurred at the SZ on the Al side for all specimens. The impact of the microstructure change in the FSW zones was significantly pronounced in the micro-indentation hardness measurements. This was presumably attributed to the promotion of various strengthening mechanisms, such as grain refinement due to DRX (CDRX or DDRX), the appearance of intermetallic compounds, and strain hardening. The aluminum side underwent recrystallization as a result of the heat input in the SZ, but the stainless steel side did not experience recrystallization due to inadequate heat input, resulting in grain deformation instead.