Is anyone going to mention that the word for ministry looks like Wizard? This is the ministry of magic people!
That's how I remember it. And the word for minister basically just swaps the vowels: waziri.
I think of "vizier" in English, a word coming from Arabic, meaning a high official. This brings me to "wizara" and "waziri", knowing that in Arabic they swap vowels to make a different word from the same root. It then helps me to think that the person starts with wa- like in the m-/wa- group, although this is a word from the ji-/ma- group. Thus "waziri" is the minister (mawaziri in plural) and "wizara" the ministry. Long story, but maybe of help to someone.