Ten Hag claimed Rashford was absent from United's 4-2 fourth-round win in south Wales on Sunday by saying he was ill on Friday.
🚨🔴 Ten Hag: “Marcus Rashford case is closed”.— Fabrizio Romano (@FabrizioRomano) January 31, 2024
“Marcus has taken responsibility and for the rest it's an internal matter. Case closed”.
“Lack of respect? Nothing to do with that. The statement is clear and we have to focus on winning football games”. pic.twitter.com/3KI1Ttjehd
But reports over the weekend suggested the England forward had spent Thursday evening at a Belfast nightclub before missing training with United the next day.
"He reported ill," Ten Hag said after United blew a two-goal lead before surviving their trip to fourth-tier Newport. "The rest is an internal matter. I deal with it, we will deal with it."
Rashford, 26, has scored just four goals so far this season, with his off-field conduct leading to fresh criticism.
Ten Hag branded Rashford's decision to go to a nightclub party after October's 3-0 derby defeat by Manchester City "unacceptable" .
The Dutch boss said there was a "no good culture" when he arrived at United and he has encountered disciplinary issues during his Old Trafford tenure.
United winger Jadon Sancho returned to Borussia Dortmund on loan earlier this month after falling out with Ten Hag.
Rashford was also dropped for a Premier League match against Wolves last season after turning up late to a team meeting when he overslept.
Ten Hag, speaking ahead of Thursday's match against Wolves, said of Rashford's recent conduct: "He has taken responsibility and for the rest it's an internal matter — case closed".
Pressed on the issue, Ten Hag repeated "case closed".