The forward missed the Red Devils' 4-2 win over Newport County on Sunday having been pictured partying in Belfast a few days earlier.
Man United boss Erik ten Hag said Rashford was ill for the team's training session on Friday, however, it later emerged that the player had been out on the town in Northern Ireland the night before.
He didn't travel with the team for their Cup clash but reported for training on Monday to hold talks with Ten Hag over his recent conduct.
It's understood Rashford will be fined two weeks' wages but the club has released a statement insisting the matter is now closed having been dealt with internally.
Man United also confirmed that the player is back in training and is available for selection for their Premier League clash against Wolves on Thursday night.
READ MORE ON MARCUS RASHFORD
Simon Jordan questions Erik ten Hag's handling of Marcus Rashford situation
Ten Hag responds to question about if Rashford is part of Man United's 'no good culture'
The statement read: "Marcus has taken responsibility for his actions. This has been dealt with as an internal disciplinary matter, which is now closed."
This isn't the first off-the-pitch controversy from Rashford in recent times having been criticised for partying in a Manchester nightclub hours after the Red Devils' 3-0 defeat at home to Manchester City in October.
In December 2022 he was dropped for their trip to Wolves for arriving late on the matchday. He scored the winning goal after being brought on in the second half by Ten Hag.
talkSPORT understands there are concerns at that Rashford's lifestyle is having a negative impact on his form.
Most read in Football
Carabao Cup final kick-off time change confirmed as Liverpool and Chelsea face off
Virgil van Dijk casts doubt over Liverpool future after Jurgen Klopp announcement
Simon Jordan questions Erik ten Hag's handling of Marcus Rashford situation
Stelling jokes low point of his career was his pronunciation being corrected by Merson
He's endured a forgetful 2023/24 season thus far having scored just four goals in 26 appearances.
Rashford has also on a number of occasions opened up on the mental health struggles he's experienced during his career.
The 26-year-old is contracted at Old Trafford until 2028 having signed a new deal last summer which is understood to see him pocket £325,000-a-week wages.