When the Wehrmacht arrived in Prague in March 1939, it was a bicycle army. The same role as USA trucks played for the Russian army in 1941-45 was played by the Czech Skoda and Tatra cars and trucks for the German army.
After the Allied invasion in Normandy the Wehrmacht had moved all motorized groups to the West and only usual infantry remained in the East. That made the huge encirclements of 1944 on the Eastern Front possible. Whole regions and republics occupied by non-mobile German troops were cut off one after another. With these troops, they couldn't even escape in time.
(It was after the Soviets reached the German lands themselves when the point of German power was turned back to the East.)
So, we can't say if the German army was motorized or not without asking what time and place we mean exactly. One of the strengths of the German and Soviet generals in WWII was that they could change not only the size and concentration of troops dynamically, but also their level of modernity. There were places where the maximally modernized and mobilized troops fought, and tens of kilometers away there were troops that looked like their WWI counterparts. Continental countries did not get the fantastical amount of technological equipment that the US army had, and they concentrated that equipment in important locations only. And as the Ardennes showed, it was more than enough.
There is another problem - motorized HOW? For example, while Stalin was preparing to the WWII in Europe in 1940-41, USSR was building "highway tanks" - with great speed, but for good roads only. But in the USSR itself there were no good roads. Even in 1989 my German far relative, a roads specialist, when he visited us in Moscow and looked around the capital, said: I haven't seen roads here, but there are places where I can drive a car. One of my acquaintances - an old Soviet officer who went by foot from Russia to Germany during WWII, had said, that along their way in all the USSR they crossed only one paved road and one asphalted. I do not remember the latitude of his way, but the main thought remains - cars in the USSR had limited use.
And in some seasons they were of no use at all. The asphalted road to Astrakhan - a regional center on Southern Volga - was built in year 1981. And before that every autumn and spring the usual ground road became unpassable. The only transport that could be used was special trucks for strategic rockets, with an engine in every wheel. And they had to travel in pairs, to help each other in harder places. (The ground is so sticky there, when wet.) In 1945 the car that could pass any Russian road simply didn't exist anywhere in the world. Even in the 90ies they said in Russia: Jeep is a car that will stuck where no other car can reach it. Another Russian proverb: Russia has two problems: fools and roads.
So, on the Eastern front it was different - tanks could run, but not too far, and with cars and trucks sometimes you had lesser speed than without them. The railway theme, raised by Michael Kay, was of extreme importance then. But the railroad mobility was not defined by the modernity of the army, but by the number of roads on the land and their defense from the air and partisan attacks.
Very important and heavily underestimated by both sides was also the river transport. Dnepr, Bug, Dnestr, were much more powerful than any rockade way.