The cars were buried in snow outside the Salang tunnel, about 80 miles north of the capital, Kabul, on the main road to the country's north, said the spokesman, Yusuf Hassan.
He said it was not clear how many people were trapped in the vehicles or if there were casualties.
The Soviet-built Salang, the world's highest tunnel at 13,350 feet, was only reopened to traffic last month. It was blocked for years by fighting.
The Afghan government asked for international assistance to rescue people in the cars and the British-led peacekeeping force in Kabul sent a helicopter to the scene, Hassan said.
But he said the United Nations does not have snowplows or bulldozers in the area.
"At least 20 vehicles have been trapped," said Yusuf Hassan, a U.N. spokesman. "The U.N. has received a request from the interim authority for assistance but we have no relevant equipment to free or rescue the people trapped there."
During the past few days, snow has blanketed parts of Afghanistan, blocking roads and isolating remote mountain villages.
Hassan said that U.N. relief agencies have emergency supplies in many large towns but are concerned that villages could run out of food if they are cut off for more than a few days.
"The snowfall is blocking off huge areas of Afghanistan," he said.
Helicopters needed to deliver vital humanitarian aid have been grounded in nearby Dushanbe, Tajikistan, Hassan said. Earlier, peacekeepers said that Kabul airport was closed due to the snow.
Millions of Afghan civilians depend on international food aid for survival.
©MMII CBS Worldwide Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press and Reuters Limited contributed to this report