It’s easy to see how Amazon.com Inc. threatens the world’s retailers. But analysts, brands and advertising agencies are waking up to the fact that a growing piece of Amazon’s business impinges on turf now controlled by two other tech titans, Google and Facebook.

Amazon’s decade-old advertising business hasn’t generated much revenue or notice until recently. One sign of the turning point was last June, at the annual meeting of advertising giant WPP PLC. Calling the retailer “highly disruptive in many ways,” WPP Chief Executive...