The Manchester Evening News published pictures of Smalling which it claimed shows the England international apparently singing "We're Man United, we'll do what we want" in the streets at 3:15am on Saturday morning.
Smalling was out injured for United's trip to West Ham on Saturday
Smalling had stayed in the north-west while the rest of his team-mates travelled to London for their Saturday evening clash against West Ham because of a hamstring injury.
Moyes is not happy with the 24-year-old's conduct, although he refused to reveal the punishment he had handed out to the player.
"I've dealt with it and I've spoken to Chris," the United boss said in a press conference. "That would be as much as I would want to say on it."
United v Olympiakos
This is not the first time the England international has found himself at the centre of controversy. The former Fulham defender was pictured appearing to dress up as a suicide bomber for a private party in January.
Smalling later apologised for the "ill-thought" and "insensitive" decision to wear the costume, which consisted of a vest, a mock circuit board, empty bottles of Jagermeister and cans of Red Bull.
The two drinks combined make up the popular 'Jagerbomb' drink.