The incident occurred at 9.20pm on Tuesday December 21 as the private jet passed over Innerleithen enroute to Dundee from London.
Aviation sources said the incident could have been catastrophic and officers are now hunting those responsible for the attack.
It is thought a powerful laser pen, which can cost less than £10, was used.
These lasers shoot beams which can reach 37,000ft, and are being used to target planes as they pass overhead, forcing pilots to cover their eyes.
In the most recent incident reported to police in the Borders, a laser was shone at an EasyJet flight as it passed over West Linton on its way to Edinburgh airport last year.
Due to the recent rise in the number of such incidents many modern airplanes are now fitted with a Laser Event Recorder which not only takes a picture of the attack but logs where it came from using GPS.
This led police in Glasgow to arrest an 18-year-old man after a police helicopter was hit by a laser beam during the Pope's recent visit. The man was eventually fined £500.
Fortunately Tuesday's targeted aircraft landed safely and it is unclear whether passengers were aware of what had happened.
A spokesman for Lothian and Borders Police confirmed that they are investigating the incident and appealed for anyone with information to contact them.