Women and children were among those killed in the accident Thursday on a major highway in Samangan province.
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"The crash happened when the bus carrying more than 50 passengers was travelling from Kabul to Mazar-i-Sharif," said Sarajuddin Fitrat, the governor of Hazrat Sultan district where the accident occurred.
"Twenty four people were killed and 17 others were injured."
The defence ministry in Kabul gave a much higher death toll of 43.
The injured were rushed to hospital while police and a rescue team retrieved the bodies.
Afghanistan has some of the world's most dangerous roads and deadly accidents are common.
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At least 18 people were killed in May when a minivan overturned in the western province of Badghis.
And in April 2013 a bus hit a wrecked fuel tanker in the southern province of Kandahar, killing 45 people.
The World Bank in November signed off a $250 million grant to upgrade roads crossing Afghanistan's Hindu Kush mountains, crucial trade links that are often closed in winter by snow.
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