This paper investigates how generative AI can potentially undermine the integrity of collective knowledge and the processes we rely on to acquire, assess, and trust information, posing a significant threat to our knowledge ecosystem and democratic discourse. Grounded in social and political philosophy, we introduce the concept of \emph{generative algorithmic epistemic injustice}. We identify four key dimensions of this phenomenon: amplified and manipulative testimonial injustice, along with hermeneutical ignorance and access injustice. We illustrate each dimension with real-world examples that reveal how generative AI can produce or amplify misinformation, perpetuate representational harm, and create epistemic inequities, particularly in multilingual contexts. By highlighting these injustices, we aim to inform the development of epistemically just generative AI systems, proposing strategies for resistance, system design principles, and two approaches that leverage generative AI to foster a more equitable information ecosystem, thereby safeguarding democratic values and the integrity of knowledge production.