How to copy a whole directory structure with a certain file size limit?

For some reasons, I need to do a data clone.

In which I need to copy the whole structure of a huge directory, but I'd like to only copy those files which are smaller than 1MB(with their hierarchy unchanged), because there are many giant temp files I want to avoid clone with.

Which utilities or commands I should use to achieve that goal?

Does zip command can realize this goal directly?