I am not aware of any standard way that the design rules for a CAD layout design are embedded into the Gerber file. Usually this information is transmitted to the PCB shop via a ReadMe type file, documented on a FAB drawing and/or entered into a PCB quote/order entry screen at the shop web site.
If you are seeing the error message that you mention via a PCB shop's automated design rules check (DRC) when you uploaded your Gerber files then there is apparently some information missing from your data set. That could be a missing drill tooling file or any one of a number of other minor details. Could even be a missing layer file in your Gerber file set.
The way to verify a Gerber file set is to open it up in a Gerber Viewer program. There are a number of viewer programs available via the Internet. Many are free for use but may require you to register with the web site in order to be able to download them.
With the Gerber Viewer program you can use its tools to line up multiple layers, scan layers to see if things look correct as per your design, and measure certain features to make sure that they are correct. Measuring can include checking certain minimum trace widths and copper to copper clearances to make sure that they are correct.
Using a Gerber Viewer is always recommended because CAD layout packages can have bugs or you may have specified certain parameters in a nonsensical way. Also when you spend many hours making a CAD layout you get used to seeing the artwork in a certain way and may miss certain details. Opening your design in another tool is like looking at it in another way and odd design details may pop right out.