The incident is believed to have happened sometime between 4pm and 7pm last Wednesday, in the Glenarch Lodge car park, on Melville Road, Dalkeith.
Officers are investigating after a 36-year-old reported being threatened at knifepoint while he was in his parked blue Subaru Impreza.
The man did not report the incident until road policing officers from Tayside Police spoke to him on Friday, after his car was involved in a collision.
Police are now keen to speak with anyone who saw anything.
A police spokesman said: “Officers are now investigating the circumstances.”