The Premier League club had said initially that the England forward, who was reportedly seen at nightspots in Belfast earlier in the week, was not well enough to be in the squad for the FA Cup match.
United said then that Rashfod had "stayed at Carrington to train as he recovers."
"He reported ill and the rest is an internal matter," manager Erik ten Hag told reporters on Sunday. "It is an internal matter. As I said, we will deal with it. I will deal with it."
United's later statement said Rashford had "taken responsibility for his actions", and the matter was now closed.
Rashford, United's Player of the Year in the last campaign, has four goals and six assists in all competitions this season.
He has been dropped before by Ten Hag, with the manager leaving him out of the starting lineup for a game against Wolves in December 2022 after he turned up late for a team meeting. Rashford ended up scoring the winner in that match.
United's next game is at Wolves on Thursday.
