The shooting took place in the car park near the entrance of Bastia airport in the north of the Mediterranean island, leaving one man dead with a gunshot to the head.
One of the injured parties was a man aged 40 who has several bullet wounds, according to French press reports. He has been reported as being in a serious condition.
Another, aged 35, received minor injuries.
Corsica was once plagued by separatist violence, but the main militant group seeking independence for Corsicans declared a ceasefire in 2014.
About a dozen assassinations of public figures have taken place on the island in the last 20 years, while murders linked to gang violence and drug trafficking have also claimed lives.
The motive for Tuesday's killings remains unclear and police are hunting for a getaway car used by the shooter.
Corsicans went to the polls last Sunday to elect a new regional assembly, which saw a triumph for nationalists seeking greater autonomy for the mountainous island.
A second round next Sunday is expected to see the nationalists confirm their victory and claim a mandate for greater local powers for Corsica, which is home to about 300,000 people and famed for being the birthplace of Napoleon.
The nationalists have vowed not to mount a bid for independence from France in the short term, unlike their counterparts in Catalonia who have provoked a political crisis by seeking to break away from Spain.