Over that timescale and without a major crash in population (which could reasonably be recovered from later), the only real option is intelligent selection.
Important note: The change in average height over the last few centuries has nothing to do with evolution. Those genes for height already existed; the thing that changed was childhood nutrition. (Less important note: this gives an important hint about why height is usually considered attractive in humans, taller people in the ancestral environment had fitter parents, indicated by the fact that they were less malnourished than everyone else.)
Evolution is very slow; the number of generations required for a new gene to become fixed in a population is equal to $2 \frac{\ln(N)}{s},$ where $N$ is the size of the population and $s$ is the increase in fitness the mutation creates. For our population of 7,000,000,000, that means 45 generations even for a mutation that outright doubles the number of children you have. Clearly, small increases in fitness like "short people are sexier" (Maybe an increase in fitness of .01, most people can find mates even if they aren't that sexy. And it's probably much lower.) just aren't going to cut it even in several thousand years.
So how could it happen? Genetic screening! Or any other sort of technology that lets parents intelligently choose which of their genes to pass on to their offspring. If a whole bunch of people have access to the technology and are influenced by similar selection criteria they could easily massively increase the fitness of those genes which they want, making it very easy for those genes to become fixed in the population very quickly.
The main question you're left with is why they'd all have that same favor towards shortness. The first thing that comes to mind is some sort of tax break or subsidy put in place by governments for people who have shorter children. They have a smaller carbon footprint and you can fit more of them in your cities, seems pretty sensible to me.