The Prussian articles of war, signed and published by the Prussian king on of 3rd August 1808 (his birthday), say:

Article 12: Those who, without permission of His Royal Majesty or the commanding general, or even against an expressed interdiction, in times of war take the property of the subjects of the enemy with force [...] or extort money or goods [...] will be punished [... according to circumstandces] even to the extend of being shot. [...]

This implies that the commanding general (but no lower ranking officers) could give the order to pillage.

Article 30: General crimes of the soldiers, i. e. transgressisons of such laws that do not have a direct relation to their military duties, will be punished according to the general laws of the country [...].

The following articles just listen the crimes, such as murder, theft, arson, rape etc. Of course, the general laws of the country in mind here are those of the Prussian states, but the oath of the soldier clearly states that he will respect the articles of war "everywhere". There is no mention of any dispensation for the times of war.

So far for the theory and legal background. I haven't checked the earlier articles of war.