The forward, on loan at Tottenham from Manchester City, fears a backlash in next Saturday's north London derby after he ran the length of the pitch to celebrate in front of Gunners' fans at the City of Manchester stadium.
Adebayor said: "Next week we play against Arsenal, the club that gave me the chance to become the player I am today. I would like to say sorry to all the Arsenal fans for the way I celebrated that goal two years ago.
"Sometimes the emotion can get the better of you, and that is what happened in this case.
"But I promise now that I will never, ever celebrate in that way again."