A homeless man's sleeping bag was set alight as he lay in it outside a shopping centre.
The 26-year-old's clothes also caught fire in the attack in Harpurhey, Manchester early on Sunday.
A 27-year-old man has been arrested on suspicion of committing arson with intent to endanger life.
Greater Manchester Police said the victim was not injured in the "shocking crime" but the clothes he was wearing were damaged.
Det Insp Tony Platten said: "This was a shocking crime which could have caused substantial injury to the victim and as such and as such I want to reassure the community and the wider public that we are treating this very seriously.
"Please let it be known that this behaviour will not be tolerated in Greater Manchester, and we are doing all we can to bring those responsible to justice."
Witnesses or anyone with information is urged to contact the force.