The front page of Thursday's edition of British tabloid The Sun showed the 24-year-old England international clad in Arab dress, including a head scarf, and with a circuit board and wires strapped to his body.
Smalling claimed that the outfit was an "attempted comedy play" on a drink known as a 'Jagerbomb', which is a mix of the liqueur Jagermeister and the energy drink Red Bull.
In a statement, Smalling's management company the Wasserman Media Group said: "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 'Jager bomb 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."
Smalling, who can play at centre-back and right-back, joined United from Fulham in January 2010 and is expected to be a member of Roy Hodgson's England squad for the World Cup in Brazil later this year.