The intrinsic magnetic low-frequency noise (LFN) is of fundamental scientific interest to the study of magnetic tunnel junctions (MTJs). To gain insight into its mechanism, the fluctuation-dissipation theorem, which describes the linear relation between magnetic LFN and magnetic sensitivity product, has been utilized. However, deviation from the linear correlation has been reported in some studies. To understand and effectively control the magnetic LFN, a more elaborate analytical description and further experimental validation are required. In this work, the magnetic LFN contributed from the magnetization fluctuation in the pinned layer of MTJs with various shape anisotropies was investigated. The MTJs with different shape anisotropies, achieved by altering their aspect ratios, possessed distinct demagnetizing factors. Large magnetic noise was correlated with the increase of magnetic phase loss of ferromagnetic layers during magnetization reversal at which magnetization fluctuation was enhanced. Upon increasing the shape anisotropy, a notable reduction of the magnetic phase loss in the antiparallel (AP) state was observed while it exhibited a slight decrease in the parallel (P) state, revealing that the increase of the shape anisotropy caused a more pronounced suppression of the equilibrium magnetization fluctuation in the AP state. These phenomena were computationally validated by constructing a macrospin model to describe the thermally-induced magnetization fluctuation in the pinned layer. This work reveals the physical relation between MTJ shape anisotropy and magnetic LFN. The effect of the shape anisotropy on the magnetic LFN can be extended to other types of in-plane uniaxial anisotropies.