The 19-year-old from Jarrow has a motif of the Olympic rings on the left side of his chest, which breaches advertising regulations.
He won his heat in the S8 100m freestyle but missed out on Sunday's final after being disqualified.
In Monday's S8 400m freestyle heats, Craig swam with a cover on the tattoo.
An International Paralympic Committee spokesman said: "Body advertising is not allowed in any way whatsoever and that includes the Olympic rings. The athlete did not wear a cover and was therefore disqualified.
