Three-dimensional object detection in panoramic imagery is crucial for comprehensive scene understanding, yet accurately mapping 2D features to 3D remains a significant challenge. Prevailing methods often project 2D features onto discrete 3D grids, which break geometric continuity and limit representation efficiency. To overcome this limitation, this paper proposes PanoGSDet, a monocular panoramic 3D detection framework built upon continuous semantic 3D Gaussian representations. The proposed framework comprises a panoramic depth estimation component and a semantic Gaussian component. The panoramic depth estimation component extracts the equirectangular semantic and depth features from the monocular panorama input. The semantic Gaussian component includes a semantic Gaussian lifting module that projects spherical features into 3D semantic Gaussians, a semantic Gaussian optimization module that refines these semantic Gaussians, and a Gaussian guided prediction head that generates 3D bounding boxes from optimized Gaussian representations. Extensive experiments on the Structured3D dataset demonstrate that our method significantly outperforms existing methods.