Large artificial intelligence (AI) models offer revolutionary potential for future wireless systems, promising unprecedented capabilities in network optimization and performance. However, current paradigms largely overlook crucial physical interactions. This oversight means they primarily rely on offline datasets, leading to difficulties in handling real-time wireless dynamics and non-stationary environments. Furthermore, these models often lack the capability for active environmental probing. This paper proposes a fundamental paradigm shift towards wireless embodied large AI (WELAI), moving from passive observation to active embodiment. We first identify key challenges faced by existing models, then we explore the design principles and system structure of WELAI. Besides, we outline prospective applications in next-generation wireless. Finally, through an illustrative case study, we demonstrate the effectiveness of WELAI and point out promising research directions for realizing adaptive, robust, and autonomous wireless systems.