The prediction is surprising on several counts. First, Amazon has notoriously limited disclosure so no one really knows much about AWS's financials. And Amazon founder Jeff Bezos, who owns 18 percent of the company, has generally brushed off criticism about some of the company's strategies—such as focusing on revenue over profits. In its relatively short life, Amazon hasn't disposed of many assets: The company has made $5.9 billion in acquisitions since 1998 but sold just $128 million in assets, according to Dealogic.
But the recent pickup in spinoff activity could mean that even Amazon will get involved, according to The Edge CEO Jim Osman. He points out that while Hewlett-Packard and eBay initially resisted breakups, they both have recently announced deals. The total value of companies that execute spinoffs is likely to reach a record $664 billion worldwide in 2014 and rise to $775 billion in 2015, according to The Edge.
Read MoreSpinoffs: 40% of them don't pay off
A spinoff could bring Amazon's value more into line with its competitors, The Edge argues. Amazon is trading at a roughly 25 percent discount to the average peer sales multiple for e-commerce companies and hardline stores, according to the note.
Another reason to separate AWS is that it could become a takeover target for companies like Salesforce.com or VMware, The Edge said. Salesforce.com declined to comment and VMware didn't respond to a request for comment from CNBC Digital.
The Edge estimates that AWS could sell for $38 billion, equating to a combined value of $195 billion for the entire company—a 36 percent upside from its current valuation.