The 26-year-old missed last weekend's 1-0 defeat to Tottenham Hotspur due to a heart scare, and could now be a doubt for this weekend's meeting with Crystal Palace after the pictures emerged in a national newspaper.
Moyes confirmed that the incident took place during the off-season, but also revealed that he has spoken to the player about his actions.
"I don't expect a player to do that, I don't expect a player playing for me to do that. I have had a word with him. I am not impressed," he told reporters.
"But I have got to also say it's a picture that comes out maybe six weeks ago, it was in his off-time, it wasn't during the season.
"But just let me make sure, in no way do I condone it at all. I think it's a bad thing for us to show our younger children and for supporters who follow the players. I don't think it's a good thing, I don't think it's a good thing at all."
Sunderland currently sit 19th in the Premier League table and are one of only two teams still looking for their first win of the season.