People were prohibited _______ their vehicles near the entrance of the main administrative building.

The correct option is "from parking".

Grammatical Rule:
In English, different verbs require specific prepositional structures or verb forms (infinitives or gerunds) to follow them. The verb prohibit is transitively used in the pattern:
prohibit someone/something from doing something.
When this pattern is used in the passive voice, it becomes:
someone/something is/was prohibited from doing something.

Step-by-Step Analysis of the Options:
1. "to park" / "to have parked": These are infinitive constructions. While some verbs of restriction like "forbid" take an infinitive (e.g., "forbidden to park"), the verb "prohibit" does not. Using an infinitive after "prohibit" is grammatically incorrect.
2. "parking": A bare gerund without the preposition "from" cannot directly follow the passive verb "prohibited" in this context.
3. "from parking": This correctly uses the preposition from followed by the gerund form parking, which perfectly completes the passive construction "were prohibited from".

Therefore, the complete, grammatically correct sentence is:
"People were prohibited from parking their vehicles near the entrance of the main administrative building."