Police said the attack happened at around 3am on Friday morning at the property in the Mount Street area of the town.
It is the latest incident following a week of disorder and attacks on properties across parts of Northern Ireland.
The PSNI said the fire at the property was started close to an oil tank at the rear which caused damage. Smoke also filled the inside of the house.
They said a man, woman and their children who were inside the house escaped.
Mount Street area of Coleraine
Photo: Olivia Peden
The incident has been condemned by local independent MLA Claire Sugden, who said it was “completely unacceptable”.
“Everyone should feel safe where they live, and no one should be targeted because of who they are. There’s no excuse for this kind of behaviour, it causes fear and tension and has no place in our community,” she said.
“The actions of a few must not be allowed to damage the character of the community as a whole,” Ms Sugden added. “Coleraine is a place where people want to live in peace with their neighbours.”
PSNI Detective Inspector Hanbidge said: “Upon officers’ arrival the fire had been extinguished by colleagues from the Northern Ireland Fire and Rescue Service.
Mount Street area of Coleraine
Photo: Olivia Peden
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“Thankfully, the house had not caught fire after an oil tank at the rear of the property had been set alight causing damage to the outside of the property. The inside of the house, however, had filled with smoke.
“A man and woman and their four young children who were inside the house at the time were thankfully able to escape uninjured.
“This, however, was a deliberate attack on a young family which could have had potentially serious consequences.
“As such, we are treating this report as arson with a racially-motivated hate element, and everyone, regardless of their ethnic background, has the right to feel safe in their home.
“Our enquiries are continuing today – with officers at the scene conducting enquiries. We are appealing to anyone who was in the area at the time and noticed anything suspicious to make contact with us.
“We also want to hear from anyone who may have CCTV, dash-cam or other footage of the area to contact police on 101, quoting reference number 144 13/06/25.”