A health brand consultancy called Arcadia Group has teamed up with Amazon to sell a new brand of consumer-focused medical devices, including blood pressure cuffs and glucose monitors, exclusively on the e-commerce giant's marketplace.

The move is part of Amazon's recent push to sell more exclusive brands on its website. It also dovetails with Amazon's increasing interest in health and wellness products and services, although Arcadia initiated this project.

"I approached Amazon last year as they began to expand their health-care footprint," Arcadia CEO Bob Guest said in a phone interview. "I felt that something that was missing from their offerings was products for people with diabetes and other chronic disease states."

Arcadia on Thursday announced that the brand for Amazon is called Choice, and that it sells things like blood pressure cuffs and glucose monitors for millions of people with hypertension and diabetes. In the U.S. alone, about 30 million people have been diagnosed with diabetes, and 1 in 3 have high blood pressure.

Guest said his company will retain the brand but sell the products only on Amazon. Arcadia Group has developed similar health brands for Walmart and other companies. (It is not to be confused with the British fashion company of the same name.)

"Choice is exclusive to Amazon but is not an Amazon private-label brand," an Amazon spokesperson told CNBC, explaining that the brand owner is in charge of the design and production.

Guest also says he's hoping to incorporate the devices his company sells with Amazon's Echo home speaker devices in coming months, which would help users manage their disease with Amazon's voice assistant Alexa. Amazon is ramping up the health and wellness team within Alexa but has not yet updated the device to be in compliance with federal privacy policies that govern how health information is stored and shared, called HIPAA.

Arcadia's Choice website also has a page where it asks people to vote on which health products it should offer next, with options such as heart rate monitors and insulin pens.

Amazon has been ramping up its private label and exclusive business in recent years, and now has over 120 brands that sell exclusively on its marketplace, according to TJI Research. SunTrust Robinson Humphrey estimates Amazon increased the number of those brands by more than nine-fold since early 2016 and is on pace to generate $25 billion in sales by 2022, up from $7.5 billion in 2018.

Amazon has been giving some private label products more exposure across its site. They now show up high in search results under a separate box titled "Top Rated from Our Brands." In recent months, Amazon has also been testing a feature that promotes its own private label brands at the bottom of its competitors' product listings.

The company has also started selling more medical products on its marketplace, including hospital supplies and over-the-counter consumer health products.

It has a business team dedicated to selling medical supplies to physician practices and hospitals, a health team within Alexa, an internal health R&D team called Grand Challenges and a pharmacy group under PillPack, which it acquired in June. It's also working with J.P. Morgan and Berkshire Hathaway to rethink health care for its own workers.