Add minimum length check to Item's custom field

Is there a way to add a minimum field length check (Ajax or otherwise) to custom text field?

I'm thinking it might involve a custom view but I do not want it on every item in the catalog.

There is no option for that in HikaShop, so yes, that will require some custom javascript added to the custom field.
You'll want to edit the file "show_block_custom_item" via the menu Display>Views in order to add your code there.
If you don't want it for all the products, simply add a check there (for example on a custom product field value).