The concept of MVP can be applied in both Agile and Lean methodologies, although it is often associated more with Lean startup methodology.
In a Lean context, an MVP is about learning what customers want with the smallest effort, reducing waste, and quickly iterating based on feedback.
In an Agile context, MVP is about delivering valuable, working software in a short timeframe, and then continually improving it in response to user feedback. This aligns with the Agile principles of iterative development and responding to change.
So, while the use of MVPs originated from Lean startup methodology, it fits well within the Agile development process, making it a useful tool in both contexts.