"We know there were 16 passengers on board," Reidar Faerestrand, police chief in Stord, told news agency Reuters.
"We are receiving preliminary information about people being transported to hospital but it's difficult to give any details at this stage," he said.
The plane was flying for Atlantic Airways, a small airline servicing Denmark's self-governing Faroe Islands in the North Sea.
The accident occurred in Stord, an island south of Bergen on Norway's western coast.
"A plane caught on fire during landing, 16 passengers were on board and it is not clear if they got out," Terje Langaas, spokesman for southern Norway's rescue centre said.