Traffic Scotland reported at 10.18am that the motorway was closed northbound at the end of the slip road at Meadowmill in Tranent due to the incident.
The car which caught fire is believed to be a Vauxhall Corsa.
Drivers were being diverted through Tranent and the second lane reopened at 10.40am.
At 12.01pm Traffic Scotland confirmed that both lanes were running again following the incident.
Police Scotland was called at 10.05am and left the scene at around 11.30am. No injuries were reported. A Scottish Fire and Rescue Service spokesperson said: “We were alerted at 10.11am on Wednesday, August 18, to reports of a car on fire at the A1 westbound near to Meadowmill and Tranent.
“Operations Control mobilised two appliances and firefighters extinguished a fire affecting one vehicle.
“There were no reported casualties and crews left after ensuring the area was made safe.”