Linguistic ambiguity is ubiquitous in our daily lives. Previous works adopted interaction between robots and humans for language disambiguation. Nevertheless, when interactive robots are deployed in daily environments, there are significant challenges for natural human-robot interaction, stemming from complex and unpredictable visual inputs, open-ended interaction, and diverse user demands. In this paper, we present SInViG, which is a self-evolving interactive visual agent for human-robot interaction based on natural languages, aiming to resolve language ambiguity, if any, through multi-turn visual-language dialogues. It continuously and automatically learns from unlabeled images and large language models, without human intervention, to be more robust against visual and linguistic complexity. Benefiting from self-evolving, it sets new state-of-the-art on several interactive visual grounding benchmarks. Moreover, our human-robot interaction experiments show that the evolved models consistently acquire more and more preferences from human users. Besides, we also deployed our model on a Franka robot for interactive manipulation tasks. Results demonstrate that our model can follow diverse user instructions and interact naturally with humans in natural language, despite the complexity and disturbance of the environment.