The vast majority of those lost customers switched to Epic Systems, the Wisconsin-based company that has long been Cerner’s chief rival. Oracle didn’t respond to a request for comment.

Epic notched its largest ever net gain in hospital market share for electronic health records, a report on Wednesday said.

A decade later, Cerner scored a huge win. In 2015, it beat out Epic, its main competitor, for a $4.3 billion contract to handle electronic health records for the Defense Department. Two years ...