Over the years numerous sports figures have received it, especially under the presidencies of George W. Bush, Barack Obama and Mr. Trump, all noted sports fans.

Just last year Babe Ruth, Roger Staubach and Alan Page were awarded Presidential Medals of Freedom. Woods will not be the first golfer to get the award; Arnold Palmer and Jack Nicklaus were honored in consecutive years in the mid-2000s, and Charles Sifford, the first African-American to play on the PGA Tour, was honored in 2014. But it is rare for an active athlete to receive the honor.

Mr. Woods has a longstanding relationship with Mr. Trump, an avid golfer. They own property near each other in Florida and have golfed together a number of times, both before and after Mr. Trump became president.

In February, Mr. Trump tweeted a picture of himself with Woods and Nicklaus at the Trump National Golf Club in Jupiter, Fla. The next day, Mr. Trump wrote on Twitter, “Tiger is back & will be winning Majors again!”