Taylor's message included a picture of four black men, one of whom seemed to be an African tribesman, in his message.
It was reported that the tweet, which has now been deleted, was in response to teasing of his attempt to learn French by team-mate Massadio Haidara.
Taylor included the Twitter accounts of fellow Newcastle players Papiss Cisse, Moussa Sissoko and Vurnon Anita in his reply to Haidara.
After the message was met with fury on Twitter by football fans, seemingly unmoved by Haidara's insistence it was just banter, Taylor tweeted: "Apologies if my tweet offended anybody."
It was thought Taylor will now be reminded of his responsibilities as a Newcastle player by club officials.