No-one would say a minstry had "made" a budget in English, so we wouldn't say one had a maker either.
You could try "creator", but "architect" or "author" would be better.
"Maker of that budget'? How about this "Our ministry is responsible for developing the budget."
To me, though awkward in English, this says "Our ministry is that budget creator." This is a very bizarre concept and I think you need to allow some leniency.