Arsonists targeted the home of a Polish family and left a "hate-filled" letter with further threats at the scene, police said.
The incident took place at the property on Blandford Road in Efford, Plymouth, overnight on Wednesday into Thursday.
A fire was started deliberately in a shed close to the house, with flames spreading to cause substantial damage.
Glass in the window of the bathroom shattered and the downpipes melted, Devon and Cornwall Police said.
After the fire was started the occupants of the property, who are originally from Poland, discovered a threatening letter had been sent to them.
Forensic examinations of the scene and letter are under way and the family are being supported by police and partner agencies.
Inspector Darren Green, of Devon and Cornwall Police, said: "I am appalled by this crime and incidents of hate such as this are treated as a priority by my officers.
"Hate crime has no place in Plymouth and we will do everything possible to locate those responsible for the fire and the disgusting letter sent to the victims.
"We believe this fire was started deliberately, was racially motivated and could have endangered the lives of the occupants.
"We are asking for the public's help in this matter as someone will know who is responsible.
"If anyone knows anything that can help with our investigations, then please get in touch.
"We would also like to hear from anyone who saw anything suspicious last night and in the moments leading up to the fire, or anyone seen fleeing the scene."
Anyone with information about the incident is asked to contact the force on 101@dc.police.uk or call 101 quoting crime log CR/045564/16.
They can also pass information anonymously to Crimestoppers by calling 0800 555 111 or report online at www.crimestoppers-uk.org.