The incident occurred around 8:30 p.m. on Tuesday evening on national highway 27 west of Gislaved.
According to the woman, the family felt that the plane was driving so low that the wheels were only slightly higher than the height of the roof of the car.
The son who was driving for practice panicked, braked and drove into the ditch.
- It is illegal to drive so low.
We were devastated afterwards, especially my son who didn't want to continue driving, says the woman.
The car that came behind also swerved into the ditch, but more controlled.
SVT has spoken to passengers in it who confirm the incident
It is unclear where the plane came from
Information from a person also states that a plane flew low also among houses in Gislaved that same evening.
A representative of a nearby flying club is unaware of the incident and says it could have been a plane from anywhere in the country.
But that a plane flying low towards a motorway could be due to engine failure which is then rectified before landing.
No one was injured in the incident.