Rashford was leaving United's Carrington training ground after traveling back from Turf Moor on the team coach.
Rashford was in a white Rolls-Royce when it collided with another vehicle.
The police were called but no ambulance was required, and the drivers did not need medical attention. Images have circulated on social media showing the scene of the incident, including damage to a lamppost and a roadside bollard.
Rashford played 90 minutes against Burnley as Erik ten Hag's team recorded their first victory in four matches.