The England international missed training at United on Friday after reporting ill and did not feature in Sunday’s 4-2 FA Cup win over Newport.
A United statement read: “This has been dealt with as an internal disciplinary matter, which is now closed.”
Rashford is back in training.
The 26-year-old will be available for selection for United’s Premier League trip to Wolves on Thursday.
“He reported ill. The rest is an internal matter and I will deal with that,” said boss Erik ten Hag after Sunday’s win in Wales.
Rashford trained at Carrington that day.
Ten Hag, football director John Murtough and interim chief executive Patrick Stewart dealt with the issue. Rashford was at United’s training ground on Monday with brother Dwaine, who is part of his representative team.
This is not the first time Rashford has been in trouble with the club this season.
He was dropped from the starting line-up for their Carabao Cup fourth-round defeat by Newcastle in November as a disciplinary measure.
On that occasion, Ten Hag was unhappy at him being seen out celebrating his birthday in one of Manchester’s most exclusive nightspots just hours after being involved in an abject 3-0 defeat by Manchester City.
Rashford was also put on the substitutes bench for United’s Premier League game at Wolves last season after oversleeping and being late for a team meeting. He subsequently scored the winner after his introduction from the bench.
The frontman has only scored four goals for United this season after hitting a career-best 30 last season.
‘He’s shown no respect for Ten Hag’
Former Manchester United defender Gary Neville told BBC Breakfast that it was about “choices and timing” when discussing Rashford’s situation.
“I would say go out and have your moment where you relax with your friends but your timing has to be right,” said Neville.
“Marcus himself knows, he’s an experienced player now. We’re not talking about a young lad but he’s done it a couple of times in the past few months.
“I’ve always seen Marcus has being really responsible, a good professional and someone who works hard every single day. I know he’s going through a dip in form at this moment in time but it’s happened twice and it can sometimes become your personality if you’re not careful.
“He just needs to relax, calm down, choose when to go out and get back to playing football at the levels we know he can.”
Former Blackburn striker Chris Sutton, speaking on BBC Radio 5 Live’s Monday Night Club, said: “Rashford hasn’t helped himself.
“I think he’ll outlast Ten Hag but this can’t go on. Something has to give. He’s shown he has no respect for Ten Hag or his team-mates. I think it’s appalling.
“Everyone knows the line. This isn’t his first misdemeanour. Why does he keep poking Ten Hag like this?”
Leicester City defender Conor Coady, who has played with Rashford for England, added: “Seeing him like this doesn’t fit, it doesn’t seem right to me. Something is there that we don’t know about.
“You see the stories coming out and wonder what’s going on? Something’s happening. To know him and realise how much of a top lad he is, you wonder is there something more to it.
“These things don’t get out at other football clubs, they only seem to get out at Manchester United. Whenever we read these things, they always seem to come out at Man United.”
Former England striker Alan Shearer said on BBC One on Sunday: “There is a huge talent in there with Rashford. We saw him be disciplined last season when he was late for a meeting and he actually missed a game, but something is clearly wrong, either at home or with his relationship with the football club, because he can’t keep doing this.
“He can’t waste his talent, it’s not right and he needs strong management and someone to get hold of him and say: ‘You know what, if you get to the end of your career and have huge regrets, you can’t have that.'”
