The tourists were driving through Kruger National Park in Skukuza, South Africa, at 6:30 a.m. Monday morning when they came upon the elephant.
The driver of the vehicle sustained serious injuries and was taken to an area hospital. The passenger was not seriously hurt.
Park spokesman William Mabasa said it was unclear why the elephant turned on the tourists.
"It is not yet clear why the elephant turned aggressive; however, we would like to appeal to the public to always be on the lookout for these huge animals and try not to get too close whenever they see one approaching on the road," Mabasa said.
By the time park rangers arrived at the scene the elephant had left. It had not been tagged so there was no way to track the animal.