How to stop AI-generated music from playing on Apple Music?

Not yet. Earlier this year Apple started using Transparency Tags that are used with submitted music by publishers/artists that cover 4 parts of AI generated content.

• Track: Flags if AI generated a major part of the audio or instrumentation.
• Composition: Flags if AI wrote a material portion of the lyrics or musical structure.
• Artwork: Flags if AI created or heavily altered the static or motion cover design.
• Music Video: Flags if AI generated a significant portion of the video visuals

We will have to wait and see how they implement filtering based on these tags. Sending Feedback as suggested by IdrisSeabright would be the way to go currently, and the link specifically for Apple Music is here.

Feedback - Apple Music - Apple

You can let Apple know you'd like to see filtering options here:

Product Feedback - Apple

No, you cannot automatically block or filter out all AI-generated music on  Apple Music The platform does not currently provide a user-facing settings toggle or filter to exclude AI-created tracks from algorithmic stations or recommendations.