The man, whose name was not immediately released but was identified by the university as a former staff member, was rushed to Harborview Medical Center with second- and third-degree burns, said Ralph H. Robinson, assistant campus police chief.
Harborview spokeswoman Susan Gregg-Hanson said the man died shortly after he was brought to the hospital.
Student Trevor Preston was walking out of a library next to Red Square when he saw the man in the middle of the plaza, pouring a liquid on himself from a large container.
"Everyone was eyeing him because we couldn't comprehend that he was actually pouring gas on himself," Preston said.
One onlooker ran toward the man in an apparent attempt to stop him, but the onlooker slipped on the liquid and did not reach the man, witnesses said.
Student Dan Kim said the man, who appeared to be alone, "lit a match and all of a sudden everything went up in flames including himself. He dropped down onto the ground. He was rolling on the ground."
Student Jacob Maria said he was in Suzzallo Library at about 1 p.m. when he heard someone scream. He came out and saw a person engulfed in flame.
Several people ran over and tried to douse the fire using their jackets or anything else they could find, Maria said, and others ran from buildings carrying fire extinguishers to help put the fire out.
"It was a huge fire. There were people running away saying 'someone just lit himself on fire,'" Maria said. "Everybody was pretty shaken up. I'm still kind of shocked that it happened."
Maria said after the flames were extinguished, the man appeared to be badly burned and not coherent when medics arrived. He said there was a strong smell of gasoline and there was a gas can in the man's backpack.
UW student Jayoung Kim said when she saw the flames she thought it was a joke, but quickly realized a man was on fire. "I started freaking out," she said.
The man was moving around, flapping his arms and rolling on the ground, Kim said.
"Nobody could do anything. We couldn't help," she said, adding that people threw clothing and tried to squirt the man with water bottles.
One man took off his jeans and stood in his boxers trying to douse the flames, she said.
Student Dan Kim said the badly burned man was mumbling incoherently when the flames were finally put out. Kim said he heard the man say "Oh my God" before he was put into an ambulance.
Robinson said it appeared to be a suicide attempt, but added: "We do not know why he did this. We do not know whether he was a student or staff or what his affiliation was."
There were no demonstrations going on at the time of the incident, Robinson said.
"It appears this was just a single event," he said.
Police evacuated Red Square and cordoned off the area for the investigation.