The move is retroactive to Monday. Floyd pitched two innings Sunday against Seattle before leaving with discomfort in his elbow.
An MRI on Monday showed no structural damage, but the White Sox decided the best plan was to put the 29-year-old on the DL.
Floyd is 9-9 with a 4.55 ERA in 24 starts.
White Sox manager Robin Ventura says ''Ax has proven he can pitch. Good choice. He's very reliable.''
Chicago also assigned outfielder Alejandro De Aza (bruised left ribs) to Charlotte on a rehabilitation assignment.