Earlier on Friday police said the emergency services had been called after a suspicious package was found outside the maternity wing of St James's Hospital, and some people had been evacuated from the area.
"A 27-year-old man from Leeds was arrested on suspicion of firearms and explosives offences, after being found in possession of a suspected firearm and a suspicious device in the hospital grounds," Counter Terrorism Policing North East said in a statement.
"He was detained for questioning and remains in custody at this time."
Searches of a vehicle and a number of premises are ongoing, they added.
Police said the incident was being treated as isolated and they did not believe there was any ongoing risk to public safety.
(Reporting by Sachin Ravikumar, Editing by Kylie MacLellan)
