The 51-year-old man was reported in critical condition when he was flown to Seattle's Harborview Medical Center, the region's trauma and burn center.
Police were not releasing the man's name, spokesman Tom Lee said.
Harborview declined to update the man's condition without a name, citing privacy laws.
The fire victim, who has only one leg, is well known to police officers who patrol downtown. He stays in shelters or lives on the streets, Lee said.
At about the same time a 911 caller reported the fire, Officer Dean Draper was nearby, questioning two men who matched the description of suspects who had robbed a woman a few minutes earlier.
Draper, who was patrolling on a bicycle when the robbery was reported, saw the two men coming from the area where the fire was reported.
The two men were later questioned by major crimes detectives and "their statements led detectives to believe the pair was involved in the fire," Lee said.
The two were subsequently arrested and booked for investigation in the robbery. The robbery victim was not injured.
The fire investigation continues, Lee said.