The 18-year-old appeared to breathe in nitrous oxide from a balloon in a video reportedly filmed a number of weeks ago.
In a statement from United, Greenwood said: “I have now been made aware of the health risks associated with this practice and accept that even trying it, as shown in these historical pictures, was poor judgement on my part. I strongly urge others not to follow my example.
“As an 18-year-old I am learning all the time, however, this week I have also learned that I will be judged to a higher standard because of my career as a footballer and I must respect that in future.
“I am determined to repay the faith shown in me by my manager and coaches.”
The pictures emerged just a week after Greenwood and Manchester City midfielder Phil Foden were sent home from England duty after breaching Covid-19 rules.
I strongly urge others not to follow my example
The duo, who made their England debuts in Iceland last Saturday, did not travel on to Denmark for Tuesday’s goalless Nations League draw.
United said at the time: “We are liaising with the Football Association and are disappointed with the actions of Mason Greenwood over this situation.”
Greenwood enjoyed a breakthrough season with United last term, making 49 appearances in all competitions and scoring 17 goals.