"It's nothing physical; it was personal reasons, and he will be here [Friday]," Cashman told the New York Post.
Before Wednesday's workout at Yankee Stadium, Rivera threw 25-30 pitches off the mound, then left to attend to a family matter, the Post said.
The 39-year-old right-hander, named Delivery Man of the Year on Wednesday, appeared in all three AL Division Series games against the Twins, working a combined 3 2/3 shutout innings.
Alden Gonzalez is a reporter for MLB.com. Ian Browne contributed to this report. This story was not subject to the approval of Major League Baseball or its clubs.