Amazon is competing with drugstores where it's known to win: price.

The e-commerce giant quietly launched a line of private-label over-the-counter drugs in August. Called Basic Care, the product line includes about 60 products ranging from ibuprofen to hair regrowth treatment. The products are produced by Perrigo, but serve as Amazon's store brand.

Jefferies compared prices between these products and Walgreens' and CVS' private-label over-the-counter products. Analysts found CVS' products were 20 percent more expensive than Amazon's at the median, while Walgreen's were 22 percent higher than Amazon's.

Eighty-four percent of Walgreens' products and 72 percent of CVS' products were more expensive than Amazon's Basic Care products, Jefferies found. Despite having higher net prices, the two traditional drugstores offered more discounts, Jefferies' Brian Tanquilut said Friday in a note to clients.

A Basic Care bottle of 500 tablets of 200-milligram ibuprofen cost $8.05 on Amazon on Friday, CNBC found. A bottle of Well at Walgreens ibuprofen pills cost $17.99 on the drugstore's website, while a CVS Health bottle cost $15.99.

Amazon's known for taking razor-thin profit margins in order to price products lower than competitors. Applying this tactic to health products could pressure drugstores who are already losing so-called front-end sales to Amazon as people buy household goods online.

Some experts have warned it could take time to change people's shopping behaviors and convince them to stock up for possible future illnesses online. Yet soon Amazon will likely be able to offer both over-the-counter drugs and prescription drugs.

It's acquiring online pharmacy start-up PillPack for roughly $1 billion. The deal threatens to remove one of the few distinguishing factors pharmacy chains have relied on to fend off Amazon, the sale of prescription drugs.

Jefferies' Tanquilut downgraded Walgreens last week after the news, which came just as Walgreens announced results from its most recent quarter. The drugstore chain reported soft same-store sales numbers, particularly in the front of the store, where over-the-counter drugs, household items and greeting cards are sold.