An artifact repository is needed but the artifact repo is a conceptual piece an not always a distinct tool. With Jenkins you should have MD5 signatures and (I think) a way of downloading the files you want (web service call, right?) from your remote server. Certainly, if you're doing something simple like using the Jenkins build pipeline plugin, it should be able to access the right versions of the files smoothly.
Alternatively, if you are using a separate deployment tool, the better ones bundle an artifact repository.
Regardless, you want what the ITIL folks call a Definitive Media/Software Library. Definitive in that the bits are secure, trusted, and official. And a library in that they can be easily looked up and accessed. When working with an artifact repository, you need to make sure its adequately secure. It is backed up. It is accessible for your deployments (including to production). If you look at Jenkins and it meets your criteria in those categories, consider yourself done. If it's lacking, and I wouldn't be surprised if it was, then you need either a dedicated tool like the Maven repos, or something bundled with the deploy tooling.
For more of my rambling on the subject, there's a recorded webcast. The slides for that are up on Slideshare.