A photograph of Smalling in the costume, which his management company said was taken at a private party in his home, appeared on the front page of The Sun on Thursday.
The England international's outfit appeared to include a mock circuit board and mobile phone around his chest, and cables leading up his body.
Also on the 24-year-old's body were bottles of Jagermeister and cans of Red Bull, while he also wore an Arab kaffiyeh head dress.
Smalling's management group - Wasserman Media Group - said the outfit was an elaborate pun on the popular "Jagerbomb," which is a blend of those two drinks.
A statement from Wasserman Media Group read: "Chris and his girlfriend hosted a fancy dress party to celebrate Christmas and their belated birthdays with close friends in the assumed privacy of his own home.
"He dressed in a costume consisting of empty bottles of Jagermeister and cans of Red Bull strapped to his chest in an attempted comedy play on the popular 'Jagerbomb drink'.
"Although he fully accepts in hindsight it was an ill-thought out and insensitive decision, absolutely no harm was intended whatsoever and he apologises for any offence caused."