Hugging Face Spaces (Spaces) has become a leading platform for hosting AI applications, offering developers seamless integration of Git-based repositories and out-of-the-box web service deployment. However, as its adoption continues to expand, security concerns have come to light. Recent reports have pointed to the issue of accidental exposure of sensitive information, such as API tokens and database credentials, within Spaces-hosted code. Despite these concerns, the research community still lacks a comprehensive understanding of the scope and impact of these security risks. To bridge this gap, we present the first large-scale and systematic empirical study to quantify the extent of secret leakage in Spaces. We begin by compiling a comprehensive dataset of 313,647 public Spaces repositories created between March 2022 and December 2024. To detect exposed secrets, we introduce Secret Reviewer, an advanced framework that combines static analysis and Large Language Model (LLM)-assisted detection to identify leaked credentials. Applying Secret Reviewer, we identified 9,149 with secret leakage vulnerabilities and 11,557 unique keys—76% of which from leading AI service providers such as OpenAI and Groq. Our findings indicate that 30% of leaks were embedded in commit histories, and over 1,000 non-code files contained sensitive data. Further validation revealed that 30% of detected keys remained active, including 140 valid database credentials and 50% of access tokens with write permissions, underscoring significant security risks. Our study sheds light on critical security challenges in AI platform ecosystems and advocates for stronger security practices to mitigate these risks.