The incident happened just before midnight on Tuesday, June 8, and officers have said that while significant damage was caused, the fire could have easily spread further.
No-one was injured but police are now keen to hear from anyone who was in the area at the time of the incident.
Detective Liam Myers, said: “This was a reckless and dangerous act and we're carrying out enquiries in the local area.
“We’re appealing to anyone with information on the fire which could assist our enquiries to please come forward.
"We're also looking to hear from anyone who was in the area and may have seen anyone suspicious around the time of the incident or anyone in Greenlaw who has CCTV.
"We are particularly interested in two silver or white BMW / Audi type saloons which were seen in the area at the time"
If you have any information on the incident you should contact Police Scotland on 101 quoting incident number 0055 of June 9.
If you would like to report information anonymously you can contact Crimestoppers on 0800 555 111.