By Agence France-Presse
No one was injured but aviation authorities will send safety inspectors to the western city of Osaka to investigate, said national broadcaster NHK.
The piece fell on the vehicle shortly after the KLM Royal Dutch Airlines Boeing 777 with 321 passengers on board took off from Kansai International Airport bound for Amsterdam on Saturday.
The panel damaged the car's roof and broke its rear window, NHK said.
The panel, 0.6 metres (two feet) long and one metre wide, is made of composite materials and fell from the base of the right wing, Kyodo News said.
It is believed to have fallen at an altitude of 2,400 metres or higher.
KLM said the aircraft landed safely at Amsterdam's Schiphol airport Saturday afternoon.
"KLM regrets this incident and has immediately launched an investigation into the causes," it said in a statement, adding that it is in close contact with Japanese aviation authorities and Boeing.