EBay Inc. is accusing Amazon.com Inc.’s sales reps of trying to poach sellers for its own marketplace through eBay’s messaging system.

EBay sent a cease-and-desist letter to Amazon on Monday to stop the alleged recruiting practice after determining roughly 50 Amazon sales representatives world-wide sent more than 1,000 messages to sellers on its platform, according to the letter, which was viewed by The Wall Street Journal, and a person familiar with the investigation.

EBay...