In recent years, there has been an upwelling of artificial intelligence (AI) studies in the health care literature. During this period, there has been an increasing number of proposed standards to evaluate the quality of health care AI studies. This rapid umbrella review examines the use of AI quality standards in a sample of health care AI systematic review articles published over a 36-month period. We used a modified version of the Joanna Briggs Institute umbrella review method. Our rapid approach was informed by the practical guide by Tricco and colleagues for conducting rapid reviews. Our search was focused on the MEDLINE database supplemented with Google Scholar. The inclusion criteria were English-language systematic reviews regardless of review type, with mention of AI and health in the abstract, published during a 36-month period. For the synthesis, we summarized the AI quality standards used and issues noted in these reviews drawing on a set of published health care AI standards, harmonized the terms used, and offered guidance to improve the quality of future health care AI studies. We selected 33 review articles published between 2020 and 2022 in our synthesis. The reviews covered a wide range of objectives, topics, settings, designs, and results. Over 60 AI approaches across different domains were identified with varying levels of detail spanning different AI life cycle stages, making comparisons difficult. Health care AI quality standards were applied in only 39% (13/33) of the reviews and in 14% (25/178) of the original studies from the reviews examined, mostly to appraise their methodological or reporting quality. Only a handful mentioned the transparency, explainability, trustworthiness, ethics, and privacy aspects. A total of 23 AI quality standard-related issues were identified in the reviews. There was a recognized need to standardize the planning, conduct, and reporting of health care AI studies and address their broader societal, ethical, and regulatory implications. Despite the growing number of AI standards to assess the quality of health care AI studies, they are seldom applied in practice. With increasing desire to adopt AI in different health topics, domains, and settings, practitioners and researchers must stay abreast of and adapt to the evolving landscape of health care AI quality standards and apply these standards to improve the quality of their AI studies.