The Manchester Evening News published pictures of Smalling which it claimed shows the England international apparently singing in the streets at 3:15am on Saturday morning.
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.
"That would be as much as I would want to say on it."
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.
- Sports & Recreation