A user, believed to be a man from Derbyshire, referred to the Chelsea star as a "choc ice" on the site.
Derbyshire police said it was investigating the original tweet after receiving complaints from members of the public.
The "choc ice" term is understood to mean "black on the outside, white on the inside".
A spokeswoman for Derbyshire Constabulary said: "We have received complaints from members of the public regarding alleged racist comments made on a social networking site.
"These concerns will be fully investigated to establish whether any criminal offences have been committed."