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 Newcastle 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."
Meanwhile, Dutch side Den Bosch have apologised to Jozy Altidore after a section of their fans racially abused the American striker.
The former Hull player, now at AZ Alkmaar, was abused during last night's KNVB Beker match and Den Bosch promised to catch and punish those responsible.
The game was stopped by referee Reinold Wiedemeijer, but Altidore himself asked for it to be continued and he scored with a penalty. He has won praise for his calm response to the situation.
Den Bosch issued a statement on their official website branding those fans who abused him "hooligans".
They said the club was "upset and disappointed" at the abuse which left "scars" on the club.
Den Bosch director Peter Bijvelds, who had addressed the crowd at half-time with an appeal for the abuse to stop, said: "FC Den Bosch will, aided by all those people who do good for their club, do everything in their power in the coming period to bring the perpetrators to justice.
"They do not belong in De Vliert [the Den Bosch stadium] and will have the most severe sanctions imposed on them."
Den Bosch fans also caused trouble in the second half, with the match halted again when snowballs were thrown at an official.
Altidore said after the match that he felt it was right to continue playing and not to respond to the insults.
He said: "I feel like I have an obligation as a football player, to my club, to my family, to not react to things like this and to show that the club stands better than that, that I was raised better than to respond to such ridiculous behaviour.
"All I can do is pray for them and hope they become better people."