The 12-time all-star, who is preparing for surgery to repair a torn knee ligament suffered last week, told reporters he spent Monday night in the hospital after doctors diagnosed the blood clot.
He was treated with blood thinners and released.
"I'm OK," Rivera told MLB.com, adding that the diagnosis "scared" him.
"I've never heard anything good about blood clots," he said.
The Yankees right-hander tore the anterior cruciate ligament in his right knee last week while shagging balls during batting practice at Yankee Stadium, ending his 2012 season.
He told the New York Daily News the knee injury may have been a "blessing" because without the doctor visits it necessitated he wouldn't have known about the blood clot.
"I always say that things happen for a good reason," Rivera said. "I was more concerned with the blood clot than the knee. For a minute, I was like, 'What else can happen?' To me, it's a blessing."