It depends on your preference and how you plan to consume the milkshake.
If you want to enjoy the milkshake immediately or within a few hours, you can keep it in the fridge. Refrigeration will help maintain its cold temperature and prevent it from spoiling quickly. However, please note that milkshakes may separate or become less creamy if left in the fridge for an extended period. Shake or stir it before drinking if that happens.
On the other hand, if you want to save the milkshake for a longer period, such as for the next day or beyond, you can put it in the freezer. Freezing the milkshake will preserve it for a longer time. When you're ready to consume it, take it out of the freezer and let it thaw for a while or blend it again to restore its creamy texture.
If you choose to freeze a milkshake, consider using a freezer-safe container and leave some space at the top for expansion as the liquid freezes. Additionally, remember that the texture might slightly change after freezing, so it may not be as smooth as when freshly made.