Rashford was spotted at Chinawhite nightclub just a few hours after United were beaten 3-0 by Manchester City at Old Trafford, a result that heaped more pressure on Ten Hag amid the club's awful start to the season.
While it has been suggested it was a pre-planned event to celebrate Rashford turning 26, the United boss revealed he has spoken with the forward about the incident and has received an apology.
“Yes I am aware of it, I spoke with him about it," Ten Hag said.
"It is unacceptable. I told him, he apologised and that is it. It is an internal matter.”
Ten Hag insisted that Rashford was not dropped for the midweek Carabao Cup defeat to Newcastle and was instead rested as the squad was rotated. The Dutchman did not provide an answer when asked if the Englishman has been fined, but confirmed Rashford is available to face Fulham on Saturday.
It has been a frustrating season so far for the forward, who has scored just one goal across ten Premier League appearances and is yet to get off the mark in Europe.
It is also not the first time Rashford has found himself in trouble with Ten Hag. He was named on the bench against Wolves on New Year's Eve last year, after turning up late to a team meeting.
However, the United boss hit back at the suggestion that this latest episode was proof that Rashford was not responding to the manager's demands.
"As I say, it is an internal matter," Ten Hag continued.
“He is fitting in. He is very motivated to put things right. I know how much effort he is putting in. He makes a mistake but that doesn’t say he is not fitting in.
“He is totally with us. He makes one mistake but also off the pitch what he is doing, how he lives, I am sure he is doing everything right to help the team and to perform and let us win.”