Vietnamese tour guide Tran Van Nghiep was driving Van Der Geest, a Dutch tourist, 23, on a motorbike up the mountain pass in Meo Vac District at around 3 p.m. when rocks came tumbling down on them.
Both men were badly injured and rushed to a local hospital for treatment, media reports said.
Another Vietnamese tour guide and a foreign tourist driving alongside them were not hit.
Many districts in the mountainous province, including Meo Vac, have experienced prolonged downpours over the past few days, triggering flooding and landslides.
Ha Giang, around 240 kilometers (150 miles) to northwest of Hanoi, is known for captivating hills and mountain passes. The Ma Pi Leng mountain pass, which runs 20 kilometers to a mountain peak two kilometers high, is considered one of the toughest trails in Vietnam.
In November 2017, a Spanish traveler died after driving his motorbike off a cliff on the pass.