Officers were called to the Jubilee Wing entrance just before 6pm yesterday (Thursday)
A man with a screwdriver was causing damage to a unit and making threats.
A fire was started which affected the A&E and X-Ray departments.
Patients and staff were evacuated from the building, but nobody was injured in the fire.
A 43 year old man was arrested on suspicion of arson with intent to endanger life.
He remains in police custody today.
Detective Inspector James Entwistle of Leeds CID said: "This was a very serious incident which caused significant damage to the hospital.
"Luckily no one was injured and everyone in the hospital was safely accounted for.
"I would like to appeal to anyone who was impacted by the fire in either the A&E or X-Ray department between 5 and 6pm to come forward with any information to assist our enquiries."
Anyone with information is asked to contact police on 101 or use the contact options at www.westyorkshire.police.uk/contactus quoting log 1301 of 21 January.
Information can also be given anonymously via Crimestoppers on 0800 555 111
West Yorkshire Fire and Rescue Service also issued a statement this lunchtime about the fire.
A spokesperson said: "We were called at 17.48 hours yesterday, Thursday 21 January, to reports of a fire in a hospital on Clarendon Way, Leeds.
"Six fire engines attended – two each from Leeds and Hunslet fire stations, one each from Moortown and Stanningley – plus the aerial appliance from Bradford Fire Station.
"Crews used eight breathing apparatus, four hose reels and a PPV fan to tackle the fire. They also assisted hospital staff with an evacuation.
"No one was injured and the fire did not spread.
"Crews left at 20.29.
"Investigations are continuing into the cause of the fire.
"The police also attended."
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