The midfielder, 25, who earns £90,000 a week, was snapped in the top of his London rivals on a trip to his native Ghana.
Essien explained his Gunners gaffe saying: "The shirt is one I swapped with Emmanuel Adebayor after a game last season.
"I gave it to my pal Eric. A girl asked for a photo. I didn't want to do it bare-chested - so Eric lent me the shirt."