General manager Brian Cashman said that the 41-year-old called him on Monday evening and explained that his children are experiencing flu-like symptoms at home.
"His kids have been sick," Cashman said. "He's hoping everything stabilizes so he can come on down.
"His intentions are to get here as soon as possible, when everything is settled with his family. We'd like to have his leadership around, but the most important thing is to take care of his family."
Cashman said that it was no problem to grant Rivera the additional time. The Yankees had initially expected Rivera to join the team in time for Wednesday's workout, but Cashman said on Wednesday morning said that the right-hander's expected arrival had been pushed back to at least Thursday.
Rivera typically has a light Spring Training workload anyway, pitching only a handful of innings and never dressing for Grapefruit League road trips.
"Even when he's here, he's got a different program, and it's obviously one that works," Cashman said.
Cashman added that the Yankees are also without right-hander Hector Noesi, who is having visa issues.
The Yankees also lost right-hander Brian Schlitter on Tuesday, as he was claimed by the Phillies. Schlitter was designated for assignment on Monday to create room on the 40-man roster for outfielder Andruw Jones.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.