The 26-year-old was absent on Friday having been spotted at a nightclub in Belfast the evening before, which initially prompted Erik ten Hag to say the player was suffering from illness.
However, it soon emerged that Rashford was facing disciplinary proceedings from his club.
Ten Hag left him at home for Sunday's FA Cup win at Newport and vowed to "deal with" the situation.
In a statement released on Monday night, United described the matter as "closed".
It read: "Marcus has taken responsibility for his actions. This has been dealt with as an internal disciplinary matter, which is now closed."
Rashford had previously transgressed when spotted partying hours after a derby defeat to Manchester City in November.
But he returned to training this week ahead of United's trip to Wolves on Thursday, which he is set to be in contention for.