Major League Baseball does not provide statistical information on races. The problem would be that defining race (even self-defining by the players themselves) would in many cases be purely subjective.
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On Opening Day in 2013, thirty teams each had 25 players on their roster -- or 750 players. Of these, 8.3% self-indentified themselves as black or African-American, 2.1% as Asian. This means 89.9% were Caucasian, or about 674.
In other words, the vast majority of MLB players are white.