It looks like it's coincidence. In Science and the Paranormal (1983), astronomer George O. Abell writes, "The moon's cycle of phases is 29.53 days, while the human female menstrual cycle averages 28 days (although it varies among women and from time to time with individual women); this is hardly even a good coincidence! The corresponding estrus cycles of some other mammals are 28 days for opossums, 11 days for guinea pigs, 16 to 17 days for sheep, 20 to 22 days for sows, 21 days for cows and mares, 24 to 26 days for macaque monkeys, 37 days for chimpanzees, and only 5 days for rats and mice. One could argue, I suppose, that the human female, being more intelligent and perhaps aware of her environment, adapted to a cycle close to that of the moon, while lower animals did not. But then the 28-day period for the opossum must be a coincidence, and if it is a coincidence for opossums, why not for humans?"
Then again, who knows? People have figured there was a connection between the lunar month and menstruation for as long as women have been getting the monthlies. Moon, month, and menstruation are all related etymologically. No less an authority than Charles Darwin believed that menstruation was linked to the moon's influence on tidal rhythms, a legacy of our origin in the sea. The coincidence between the lunar and menstrual cycles is closer than George Abell would have us believe--studies have found the average menstrual period is 29 days and change. At least some critters' biologies are linked to the lunar cycle; in the lemur, for example, estrus and sex tend to occur around the time of the full moon.
Efforts to turn up similar patterns in humans have had unimpressive results, however. Several researchers over the years have claimed to detect lunar rhythms in menstrual onset and such; others see nothing. Biologist Winnifred Cutler, in a 1980 paper, found that 40 percent of women in a random sample showed "a preponderance of menses onsets in the light half-cycle of the month" (the two weeks centered on the full moon). To me this suggests 60 percent of the women didn't show any coincidence. If there really is a moon-menstruation link, it hasn't been convincingly proven yet.