Yes. If the medical editor does not qualify for authorship (read how the International Committee of Medical Journal Editors [ICMJE] defines authorship here), you should acknowledge their contributions to your publication in the Acknowledgments section. The ICMJE gives examples of contributions such as writing assistance, technical editing, language editing, and proofreading.
My professional organization, the American Medical Writers Association, has a position statement on the contributions of medical writers to scientific publications that also encourages acknowledgment. It reads,
The American Medical Writers Association (AMWA) recognizes the valuable contributions of biomedical communicators to the publication team. Biomedical communicators who contribute substantially to the writing or editing of a manuscript should be acknowledged with their permission and with disclosure of any pertinent professional or financial relationships. In all aspects of the publication process, biomedical communicators should adhere to the AMWA Code of Ethics.
The European Medical Writers Association (EMWA) also suggests that the “role of medical writers must be transparent, which normally means a mention in the acknowledgements section.”
The instructions for authors of the journal to which you are submitting your manuscript may also mention who should be acknowledged, usually in conjunction with a discussion of authorship. For example, the JAMA Instructions for Authors reads, “All other persons who have made substantial contributions to the work reported in the manuscript (eg, data collection, analysis, and writing or editing assistance) but who do not fulfill the authorship criteria should be named with their specific contributions in an Acknowledgment in the manuscript.”
When I return an edited file, along with tips on how to deal with track changes, I also write,
My professional organization, the American Medical Writers Association, and the ICMJE encourage authors to acknowledge the contributions of medical writers and editors. Kindly consider acknowledging me for language editing or medical editing.
Acknowledging your medical editor is not just good publishing practice. An acknowledgment is welcome feedback for the editor's diligent work and is sure to engender goodwill.