No. It causes no wear of any significance whatsoever.
In classic (non-SSD) hard drives the magnetic material on a drive's platters might eventually "wear out" and lose it's ability to store magnetic charges after a ridiculously huge number of writes, but hard drives will fail long before that due to mechanical failure.
Classic hard drives suffer the most wear during spin-up and when doing excessive head movements. Formatting is no different than writing to the hard drive normally. In addition to that, normal usage writes to the same general area of a drive very often and requires lots of head movements whereas formatting will sequentially overwrite the entire hard drive, writing each location only once.
Whether or not it is SSD, the more usage of a drive will reduce its life. However a format once a month isn't going to do much compared to any other program.
I'd suggest figuring out why you are formatting and reinstalling once a month and trying to solve that.
If you 'like' to format and reinstall, then think about using a disk imaging software such as Ghost, or install Windows 7, create a system image, and then restore from backup, save yourself some headache.