Police said army specialists attended the scene and a cordon was put in place as a precautionary measure.
A bomb disposal unit was also at the scene, with some wearing protective equipment.
The wing is home to the majority of the hospital’s maternity services, as well as some respiratory and bereavement services.
People have been asked to avoid the entrance to the maternity wing while the cordon remains in place, after some ward areas were evacuated to keep “patients and staff safe”.
CTP North East said a suspect from Leeds has been arrested in connection with the incident.
In a statement, the Leeds Teaching Hospitals NHS Trust said: “A cordon has been put in place as a precautionary measure to ensure public safety and we have been working with the police to evacuate some ward areas to keep our patients and staff safe.
“Patients are being asked to attend hospital as normal for appointments, unless they are contacted otherwise.
“Visiting for patients who are currently in Gledhow wing and Lincoln wing at St James’s Hospital is suspended until we have more information.”
The trust said the accident and emergency department remains open.