Self-recognition -- the ability to maintain an internal representation of one's own body within the environment -- underpins intelligent, autonomous behavior. As a foundational component of the minimal self, self-recognition provides the initial substrate from which higher forms of self-awareness may eventually emerge. Recent advances in large language models achieve human-like performance in tasks integrating multimodal information, raising growing interest in the embodiment capabilities of AI agents deployed on nonhuman platforms such as robots. We investigate whether multimodal LLMs can develop self-recognition through sensorimotor experience by integrating an LLM into an autonomous mobile robot. The system exhibits robust environmental awareness, self-identification, and predictive awareness, enabling it to infer its robotic nature and motion characteristics. Structural equation modeling reveals how sensory integration influences distinct dimensions of the minimal self and their coordination with past-present memory, as well as the hierarchical internal associations that drive self-identification. Ablation tests of sensory inputs demonstrate compensatory interactions among sensors and confirm the essential role of structured and episodic memory. Given appropriate sensory information about the world and itself, multimodal LLMs open the door to artificial selfhood in embodied cognitive systems.