A 39-year-old man from Gateshead was detained on suspicion of posting the offensive comments about the former Newcastle player.
He has been arrested on suspicion of racially-aggravated harassment and bailed pending further inquiries.
Ba, who joined Chelsea at the start of the transfer window, is likely to be back in the north-east this weekend as his new club is facing his old one 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."