The striker on Friday missed training after calling in sick amid reports he had attended a nightclub in Belfast the previous evening.
Photos and footage circulated on social media allegedly showing Rashford attending Thompsons nightclub, with The Athletic reporting the images were taken on Thursday evening.
United players had a scheduled day off earlier in the week, the same day Rashford was photographed in Belfast bar Lavery’s. The Sun reported that Rashford was in Northern Ireland visiting friend and former United academy team-mate Ro-Shaun Williams, who plays for Larne FC.
Speaking to BBC Sport ahead of United's FA Cup clash at Newport, Ten Hag said of the absent Rashford: "He reported ill".
Pressed further on speculation Rashford had been partying, Ten Hag added: "It's an internal matter. I deal with it."
BBC Sport pushed again for the manager to elaborate, who replied in frustration: "Listen, it's an internal matter. Internal matter."