Manager Aaron Boone made the announcement Monday but said a trip to the injured list is still possible for Chapman.
"I think the IL is still very much in play. I just think we don't want to rush into it. ... We'll kind of see what we got," Boone said.
Chapman allowed a tiebreaking homer to AJ Pollock in the ninth inning of New York's 3-1 loss to the Chicago White Sox in Game 1 of a doubleheader Sunday in the Bronx. The seven-time All-Star has now allowed runs in five straight appearances, the longest streak of his career.
Speaking through an interpreter, Chapman said he's been receiving treatment on the Achilles for a couple of weeks. Asked how much it's affected him, he added: "When you're dealing with things, sometimes it can affect you, but at the end of the day, it's not the reason for the last results.
"Pretty simple, things have not worked out the way I would want."
Chapman is now 0-2 on the season with nine saves and a 3.86 ERA.