Greenwood had been facing charges including attempted rape and assault, but prosecutors said the case had been discontinued following the withdrawal of key witnesses and “new material that came to light”.
United issued a statement on Thursday saying the club would now “conduct its own process before determining next steps”.
In a short statement released on his behalf, Greenwood said he was “relieved the matter is now over”.
At a pre-match press conference on Friday, Ten Hag refused to be drawn on the subject.
“I can’t add anything,” said the Dutch manager, in his first season at Old Trafford. “I refer to the statement of the club.”
Greenwood, who has two and a half years left on his contract, has been suspended from both training and playing for United since his arrest in January 2022.
But with United still involved in four competitions, Ten Hag is keen for his players to be focused on the job at hand.
“That’s our job, not to get distracted by anything,” Ten Hag added. “We are human beings and sometimes there are issues, we are not like robots, but we have to focus on our job.
“We have so many games so we don’t have time to get distracted by anything. It’s not easy but that is our job.”
Ten Hag has been credited with transforming United’s fortunes as they sit fourth in the Premier League and reached the League Cup final this week for the first time in six years.