The precision and accuracy of the final geometry in micro-parts is crucial, particularly for high-value-added metallic products. Micro-extrusion is one of the most promising processes for delivering high-precision micro-parts. The curving tendency observed in micro-extrusion parts is a major concern, significantly affecting the final part geometry. The purpose of this paper was to investigate the driving mechanism behind the curvature in micro-extrusion at room temperature. A finite element (FE) simulation was carried out to observe the influential primary factors: (1) grain size, (2) grain boundary, (3) grain orientation, and (4) bearing length of a 6063 aluminum alloy. The Extrusion Curvature Index (ECI) was also established to indicate the level of curvature in micro-extruded parts. The results showed that the grain boundary at the high strain and die opening area was the dominant factor for single-grain conditions. The interactive effects of the grain boundary and grain orientation also affected the curvature under single-grain conditions. If the number of grains across the specimen increased up to 2.7 (poly-grains), the curvature effect was dramatically reduced (the pins were straightened). For all conditions, the curvature in micro-extrusion could be eliminated by extending the bearing length up to the exit diameter length.