We show the possible existence of a significant axial asymmetry in the reconnection separator at the Jovian magnetopause using first‐principle, physics‐based global simulations. Under eastward interplanetary magnetic field (IMF) conditions near Jupiter's orbit, reconnection occurs at the southern‐dusk and northern magnetopause with large shear angles between the magnetospheric and magnetosheath magnetic fields. When driven by the westward IMF, the reconnection position switches to the northern‐dusk and southern magnetopause. Component reconnection at the southern‐dusk/northern‐dusk magnetopause is associated with the interaction of the IMF with the nearly‐dipolar background fields. Nearly‐antiparallel reconnection near the noon‐midnight plane at the northern/southern magnetopause is related to the dawn‐dusk asymmetric, helical, closed lobe magnetic fields, which is a consequence of significant planetary corotation effects and not expected at Earth. Such configuration is testable as Juno has proceeded its orbit to the high‐altitude cusps and provides new insight into the interpretation of measurements from other rotationally‐driven systems. Plain Language Summary: Magnetic reconnection is a fundamental plasma process for understanding the dynamic evolution of planetary magnetospheres. It is related to the breaking and reconnecting of magnetic fields from two different sources. Depending on the orientation of the interplanetary magnetic field (IMF), reconnection at a planetary magnetopause is a combination of antiparallel and component reconnection of magnetic fields in the outer magnetosphere and the inner magnetosheath. In the terrestrial magnetosphere, magnetopause reconnection that is dominated by solar wind‐magnetosphere interactions is generally symmetric about the Sun‐Earth axis in solar‐magnetospheric coordinates regardless of the IMF orientation. However, this axial symmetry may not exist in planetary magnetospheres where the time scale of planetary rotation is much shorter than the solar wind transition, especially at Jupiter that has a faster planetary rotation and a significantly larger magnetosphere than Earth's. This study focuses on an unusual asymmetry in magnetospheric configuration and magnetopause reconnection at Jupiter and its relationship with fast planetary rotation. Key Points: Unlike at Earth, magnetopause reconnection at Jupiter may exhibit a significant axial asymmetry under east‐west interplanetary magnetic field (IMF) conditionsThis asymmetry is caused by the helical, closed lobe magnetic field with dawn‐dusk asymmetry due to fast Jovian rotationReconnection may occur at northern and southern‐dusk magnetopause under eastward IMF and has a north‐south reversal for westward IMF [ABSTRACT FROM AUTHOR]