The 48-year-old man, who was a patient at Prince of Wales Hospital in Sydney, allegedly doused three other patients - two men aged 54 and 63 and a 64-year-old woman - with an accelerant about 10.45pm on Tuesday.
He then allegedly set the 54-year-old man on fire.
According to police the 54-year-old man was quickly extinguished by hospital staff and suffered minor burns.
He was in a stable condition on Wednesday evening.
The 63-year-old man and 64-year-old woman were treated for minor injuries and are both in a stable condition.
Police charged the 48-year-old man with two counts of attempted murder, common assault and two counts of attempt to cause grievous bodily harm to person with intent.
The man is due to face court for a bail hearing on Thursday.
A spokesperson for the hospital said there was no ongoing risk to patients and staff.
Staff responded quickly and immediately notified NSW Police, who responded to the incident, the spokesperson said.
"South Eastern Sydney Local Health District is offering support and care to the people impacted by this distressing incident," they said.
NSW opposition health spokeswoman Sarah Mitchell was deeply disturbed by the alleged incident.
"This is beyond unacceptable in NSW," Ms Mitchell said.
"Safety must be a non-negotiable in our public hospitals.
"My thoughts are with the victims and their families, hospital staff and first responders."
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