Cleveland Police are investigating the circumstances of the incident in Warren Road, in West View.
The force said they were alerted by the North East Ambulance Service which had treated the woman for an injury to her leg.
Warren Fisheries was surrounded by a police cordon early on Wednesday, July 20, but it was removed a short time later.
A single police car was parked outside.
A police spokesperson said: “Police were alerted by ambulance service colleagues to a woman with an injury to her leg and she received treatment.
"Inquiries are ongoing into the circumstances of what happened.
“Two people have been arrested in connection with the incident and they remain in police custody.”
The ambulance service said: “We got a call at 11.45pm to respond to an incident in the Hartlepool area.
"We dispatched a paramedic crew who took one patient to James Cook hospital.”