The incident happened at Matthewsons in Thornton-le-Dale at around 1.40am on Tuesday July 26.
Police say the fire was started deliberately after an accelerant was thrown.
One vehicle was damaged but fortunately the fire did not spread to other cars, the garage itself and nearby buildings where people were asleep inside.
Officers are already exploring numerous lines of enquiry and believe the offender may have sustained burn injuries to their arms, but this is not confirmed.
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PC Alan Robson, who is investigating the incident, said: “Thornton-le-Dale is a quiet, peaceful Ryedale village and the Matthewson family are very keen to establish who was responsible.
“We already have several strong lines of enquiry and we are now requesting the public’s assistance to track down those responsible.”
Anyone with information that could assist the investigation should email [email protected]
You can also call North Yorkshire Police on 101, select option 2 and ask for PC Alan Robson.
If you wish to remain anonymous, you can pass information to Crimestoppers on 0800 555 111. Please quote the North Yorkshire Police reference number 12220130660.