Emergency services were called to an address in the Lower Bathville area of Armadale at 2.10pm on Sunday.
The fire service was able to extinguish the blaze, which caused “substantial damage”, but no-one was hurt.
Detective constable Marc Lunn said: “Thankfully nobody has been injured as a result of the incident but substantial damage has been caused.
“We are appealing to members of the public who may have noticed anyone acting suspicious in the area to come forward and speak to officers.
“I would ask if anyone has possible dashcam or CCTV footage that could assist with our investigation to contact police.
“Police can be contacted on 101 quoting incident number 2202 of Sunday May 30 2021.”