The Manchester United full-back was forced off during Sunday’s 2-0 Nations League victory over Wales and will now return to his club for further assessment.
“We're sending him home now. He is out and won't be ready for the coming week,” Riemer said.
The Denmark manager said further examinations would be needed to determine the length of Dorgu’s absence.
“Further examinations will show how long he will be out,” Riemer said.
Dorgu’s withdrawal follows those of Alexander Bah, Kasper Dolberg and Albert Grønbæk, leaving Riemer facing a rapidly changing squad.
Bah returned home earlier in the week after suffering a setback with his troublesome shoulder, while Dolberg departed after suffering a serious knee injury.
Grønbæk then left the camp on Friday after being injured against Norway.
Riemer admitted that the sequence of injuries had left him facing a situation he had never previously experienced with Denmark.
“I don't normally cry, but this is crazy what I am involved in. I have certainly never experienced this before,” the coach said.
“In one week, we have already said goodbye to four players.”
The number of withdrawals has also created a problem with Denmark’s attacking options. Riemer said Mohamed Daramy and Gustav Isaksen could not be expected to play two full 90-minute matches during the coming week.
“We have to call up at least one more winger,” he said.
Riemer has identified several possibilities for the additional call-up, including Anders Dreyer and Andreas Skov Olsen, who has made a strong start in Turkey.
“There are several possibilities. Now we have to think carefully before we decide who we select,” he said.
The coach also highlighted AGF youngster Frederik Emmery as another option.
The Denmark camp is therefore set for another change, with at least one new player expected to be called up as Riemer attempts to replace Dorgu and manage the growing list of absentees.
Dorgu had started Denmark’s Nations League matches before his latest injury and now faces a period of assessment with Manchester United.
The club will determine the extent of the problem after his return, while Denmark must prepare for its next fixtures without one of its available wide options.
For Riemer, the immediate challenge is rebuilding his squad after four departures in a single international window.