As Shopify is not a regular web host which provides web space which you can upload files and folders (such as a Juicebox gallery) to via FTP (please see this Shopify FAQ for details), you will need to host your gallery elsewhere and embed it into your Shopify page using an iframe.
This can be done by following the Embedding in a Web Template Site instructions.

@ckukshtel

All gallery files must be hosted on the same domain or subdomain as the HTML page containing the gallery's JavaScript embedding code. This is due to the same-origin policy. Knowing that you are using Shopify and that you are unlikely to be hosting your gallery on Shopify's own web servers, then this is like to be the problem that you are encountering.
Possible solutions would be to use an iframe  (as I mentioned in my post above) or you may be able to implement a Cross-Origin Resource Sharing (CORS) solution: http://www.w3.org/TR/cors/
Try adding the following to the .htaccess file in the root directory of the domain which currently hosts your gallery.

Header add Access-Control-Allow-Origin "*"