Musial was among 15 recipients honored at the White House. President Obama called the Hall-of-Famer "a gentleman you would want your kids to emulate."
"He asked for a pay cut when he didn't perform up to his own expectations," Obama said. "You can imagine that happening today."
The honor is given to those who have made important contributions to U.S. national security, world peace, culture or other significant public or private endeavors.
Basketball great Bill Russell, the first black NBA coach, also received the honor. Obama praised Russell, who marched with the Rev. Martin Luther King Jr., for his courage and strength as a member of the Boston Celtics, where he regularly endured racism from fans.
The president described how Russell refused to play after a restaurant declined to serve the team because of its black members, and called him "someone who stood up for the rights and dignity of all men."
Musial, 90, wore his familiar Cardinal-red sports coat and beamed as the president placed the medal around his neck.
Missouri politicians said the honor was appropriate for the baseball immortal whose nickname, "The Man," was as appropriate for his philanthropy and kindness as for his on-field success.
U.S. Rep. William Lacy Clay, a St. Louis Democrat, said Musial showed great courage in 1947 by welcoming Jackie Robinson, baseball's first black player, into the National League.
"Stan Musial is a national treasure," Clay said. "His remarkable life represents the very best of America."
Musial was a 24-time All-Star who retired after the 1963 season with a .331 batting average 475 home runs and 3,630 career hits.
He was the general manager of the 1967 Cardinals, which won the World Series in seven games over the New York Yankees.
A grass-roots "Stand for Stan" campaign helped convince the White House to honor Musial. The Cardinals promoted the idea through Facebook, Twitter and other social media, and politicians quickly joined in letter-writing campaigns.