In recent years, test-time adaptive object detection has attracted increasing attention due to its unique advantages in online domain adaptation, which aligns more closely with real-world application scenarios. However, existing approaches heavily rely on source-derived statistical characteristics while making the strong assumption that the source and target domains share an identical category space. In this paper, we propose the first foundation model-powered test-time adaptive object detection method that eliminates the need for source data entirely and overcomes traditional closed-set limitations. Specifically, we design a Multi-modal Prompt-based Mean-Teacher framework for vision-language detector-driven test-time adaptation, which incorporates text and visual prompt tuning to adapt both language and vision representation spaces on the test data in a parameter-efficient manner. Correspondingly, we propose a Test-time Warm-start strategy tailored for the visual prompts to effectively preserve the representation capability of the vision branch. Furthermore, to guarantee high-quality pseudo-labels in every test batch, we maintain an Instance Dynamic Memory (IDM) module that stores high-quality pseudo-labels from previous test samples, and propose two novel strategies-Memory Enhancement and Memory Hallucination-to leverage IDM's high-quality instances for enhancing original predictions and hallucinating images without available pseudo-labels, respectively. Extensive experiments on cross-corruption and cross-dataset benchmarks demonstrate that our method consistently outperforms previous state-of-the-art methods, and can adapt to arbitrary cross-domain and cross-category target data. Code is available at https://github.com/gaoyingjay/ttaod_foundation.