It said the aircraft was flying at 5,500 feet (about 1,600 metres) as it neared Paris' Charles de Gaulle airport on February 19 when the co-pilot noticed a drone approaching on the left side.
The co-pilot disconnected the automatic pilot and carried out an avoidance manoeuvre while informing the pilot of the presence of the drone.
Drones becoming 'real' threat to commercial aviation: IATA
The pilot estimated that the drone passed about five metres under the left wing of the plane, the BEA said in a report on Thursday.
The crew immediately informed ground control and resumed their approach without further incident. The BEA described the incident as "serious".
It gave no details about the number of people on board nor the size of the drone. An A320 can carry 160 passengers.
Aviation industry group IATA warned last month that civilian drones are increasingly becoming a "real and growing threat" to the safety of commercial aviation.
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In late 2014, France was hit by a spate of mystery drones flying over French nuclear plants.
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