The four people, including a ten-year-old Finnish girl, were hurt by a loose metal part from the escalator, Ekstra Bladet reports.
A member of state rail operator DSB's press department confirmed the accident to Ritzau but was unable to give further details.
The accident occurred at 1:45pm on Sunday and involved a British citizen and a 26-year-old Dane as well as the girl and her father.
The 26-year-old described the incident to Ekstra Bladet.
“I was cut on my shin by a loos metal strip that was sticking out. It was a kind of decking strip,” the man, named only as Martin, said.
The witness also said that the 10-year-old girl and her father sustained broken legs and were taken to Copenhagen's Rigshospitalet by ambulance, while the British citizen was treated at Hvidovre hospital.
Ritzau reported on Sunday afternoon that DSB was unable to further comment on the incident and was referring further for information to Copenhagen Police. Copenhagen Police duty officer Henrik Stormer said questions should be directed to DSB.