OK, I've found a fix for the issue.
The way the car is modeled (I didn't create this model), the wheels just barely touch the ground. Here's a render of the car driving away with no motion blur. You can see the wheels just touch the ground at the peak of the curvature.
So when the wheels spin with motion blur, the gap will appear between the wheels and the ground.
However, a true car tire will have some deformation from the weight of the car so that more of the tire touches the ground, but the car tires on this model obviously don't do that.
My fix was to just slightly sink the model just a tad below the ground plane, as a true car tire would somewhat flatten a bit where it touches the ground anyway. Now, when I apply motion blur, there is no more gap.
