Organisers said Miettinen, who was 66 years old, died after a crash that stopped the race after about half an hour of the scheduled four hours. All the other drivers were taken to hospital with injuries that were not life-threatening.
Red Bull F1 driver Verstappen, sharing a Mercedes AMG GT3 sports car with Austrian Lucas Auer, was not on track at the time.
"During the first race of the ADAC 24h Nürburgring Qualifiers, a serious accident involving seven competitors occurred in the early stages of the race," Nurburgring officials said in a statement.
"Despite the immediate arrival of emergency services, the emergency medics were unable to save the driver involved, Juha Miettinen (BMW 325i, #121), after he had been extracted from the vehicle. The driver died at the Medical Centre after all attempts at resuscitation proved unsuccessful."
Organisers said the race would not resume on Saturday and a minute’s silence would be held during the grid formation on Sunday.
Verstappen said on Instagram that he was shocked by what had happened.
"Motorsport is something we all love but in times like this it is a reminder of how dangerous it can be," he posted.
"Sending my heartfelt condolences to Juha's family and loved ones."
The Nurburgring's historic and fearsome Nordschleife, known as the 'Green Hell' when it hosted Formula One in the 1960s and 70s, is a 20.8 km (12.9 miles) loop in the Eifel region of Germany. It was first opened in 1927.