Unknown at this time
I've tried to find a canon / official source of this information on and off since you asked this question. Given that I could find nothing, and given no one else seems to have, I'm ready to declare that we just don't know.
From an out-of-universe vantage point, no storyline has necessitated such an estimate, and so the writers had no need to draw themselves into a corner by making some claim that X-many humans work for Starfleet.
The question makes the assumption that Starfleet forms part of Earth's "economic structure", but through a number of questions over the past couple of years, we've more or less decided that Earth has no economic structure in the traditional sense by the 24th Century, if not earlier.
Rather, Earth has a post-scarcity economy in which mass replication has eliminated the need for the individual to maintain a traditional economic life by our standards. A human need not work for anyone, and can spend his or her time doing what is considered "fulfilling". This is consistent with the notion of Earth as a future paradise, something that is analyzed with the sharpest lens in DS9.
See these, for instance:
We know that Starfleet Academy is especially demanding, and so while humans do dominate Starfleet (it grew out of the United Earth Space Probe Agency), we would not expect many humans to have completed its primary training programmes relative to Earth's population.
That doesn't mean that Starfleet doesn't have skilled workers and enlisted non-commissioned personnel, such as Chief O'Brien, as well as various civilian support roles.
For example, we know that Starfleet maintains significant operations in San Francisco (where the headquarters are) and maintains archives in London (as shown in Into Darkness).
But again, we simply don't know the numbers.