A 39-year-old man from Gateshead was detained on suspicion of posting the offensive remarks about the former Newcastle player.
Police said he was arrested on suspicion of racially-aggravated harassment and bailed pending further inquiries.
Ba, who signed for Chelsea earlier this month, is expected to return to the North East this weekend to face his old team at St James' Park.
A Northumbria Police spokesman said: "Police received a complaint about an offensive message posted on Facebook earlier this month.
"A 39-year-old Gateshead man has been arrested on suspicion of racially-aggravated harassment and has been bailed pending further inquiries."