Fans in the left-field bleachers chanted obscenities and pointed at the man Wednesday night during the sixth inning of the game between the Indians and New York Yankees.
Hundreds of fans joined in before security led the man out of Progressive Field.
As he left, some fans followed him toward the gate with more derisive chants. Various media reports indicated he was with a female companion, and that fans also threw debris at them.
The man was shown showing off his No. 6 jersey to the crowd as he walked down the steps.
James' recent departure from the Cleveland Cavaliers to the Heat caused a lot of anger in the city.
Many fans were near the left-field foul pole in hopes of catching the 600th home run ball by Alex Rodriguez.
Information from The Associated Press was used in this report.