Huggins and Scott Auctions is handling the bidding, which started at $900 and will run through February 11.
Mourning, a seven-time All-Star who won an NBA title with Miami in 2006, wore the jersey when he played in a set of pickup basketball games at Fort McNair in Washington to celebrate Obama's 49th birthday on August 4, 2010.
Obama played in pickup games alongside and against NBA stars Mourning, LeBron James, Kobe Bryant, Carmelo Anthony, Magic Johnson, Pau Gasol, Chris Paul, Baron Davis, Chauncey Billups, Shane Battier and Grant Hill plus Women's NBA standout Maya Moore.
Several wounded US soldiers were invited to watch the games and after one contest, Mourning gave his jersey to one of them, Jack Thebau. It was later signed by Obama and the players involved.