Along with Thompson, RiverDogs pitcher Andy Beresford was also suspended.
In a press release, Major League Baseball said the pair tested positive for amphetamines.
Thompson was a 13th round pick of the Yankees in this year's draft. He was playing in the Gulf Coast Rookie League and hitting just over .200 with a homer and 10 RBI. In a statement on Twitter, Thompson said "People will love you then, turn there (sic) backs on you QUICK".
Beresford, a 19th round pick by the Yankees in 2013, had pitched in 13 games for the RiverDogs this season (including 7 starts) going 1-2 with a 4.35 ERA.