Henry clashed with the supporter following the 3-2 defeat but claimed that he iss sorry for swearing in response to the abuse.
The 34-year-old said: "So I would like to first and foremost apologise for using inappropriate language to that particular 'supporter'.
"I was really shocked and disappointed on Sunday — and not just at the result.
"When I arrived in front of our own fans, I couldn't understand the abuse the team were getting from one of them."
Henry is currently on loan at Arsenal from New York Red Bulls.