I'm going to take a stab at this question using population statistics for the UK and civil servant statistics. As I'm just about as talented as JKR with maths, please take these as estimates and approximations.
In 2011, the Office for National Statistics reported that 498,433 persons are employed in the UK in civil service. SOURCE An Excel spreadsheet detailing what branches of government are covered can be found here (and note, there is a discrepancy between the totals, but the spreadsheet does take contract employees into account, where the NOS statistics do not).
According to the Office for National Statistics, there are 62,220,000 residents in the UK. According to the CIA, there are 62,698,362 people living in the UK (July 2011). I averaged these numbers and got 62,459,181.
498,433 is 0.79801% of 62,698,362, indicating that approximately 0.80% of the total population of the UK is employed as a civil servant.
Now, there have been several numbers thrown out by JKR of how many students are at Hogwarts and what the general Wizarding population is. Since they're all over the board, I'm going to go with her original statement of there being 600 Hogwarts students. To get an estimate of the total Wizarding population, I Google-Fued and read quite a few articles on Wizarding population. For purposes of this question, I went with this essay. It's a fairly long and involved essay, but it's interesting. The original author appended the essay with additional input from a professional (scroll to the bottom). A brief excerpt:
ESTIMATED WIZARDING POPULATION BASED ON JKR'S ORIGINAL STATEMENT OF 600 HOGWARTS STUDENTS:
We have as given that the age class between 11 and 17 is approximately 600, whether Hogwarts actually accommodates them all, or whether JKR misspoke and it is actually a smaller school, educating the elite of that 600, as implied by class sizes shown in the book.
Each age class below age 20 will then contain 1/2 of 1% of the total population, and the 1000 secondary school students make up 7 x 0.5 or 3.5% of the total wizarding population, yielding a total population (1000/3.5 x 100) of about 17,143.
Varying our assumptions, in the unlikely situation that we have an increasing population, we would have a current total population of 15-16,000. Making the more likely assumption of a decreasing population, we would get a current population of as much as 20,000 but with a birth rate disastrously less than the death rate.
- Will Pratt
0.79801% of 15,000 is 119.701500
0.79801% of 17,143 is 136.8028543
0.79801% of 20,000 is 159.602
So my guesstimate is that there are between 120 and 160 Ministry employees in total, based on comparison to the population and civil servant statistics of the UK's Muggle population, using the three proposed Wizarding population estimates. Yes, these numbers seem low, but that's what came up, and I'll reiterate that JKR's maths and the numbers she throws out don't seem to be definitive.
Of course these numbers wouldn't be precisely reflective of Harry's canon years of 1991-1998 (Hogwarts era) and then 2017 (Epilogue era), but perhaps the general principle may apply. :)