actually, i have always experienced the opposite. i've done two x 14-day + a 26-day + a 36-day-to-completion fasts (for healing). i started all of those fasts just after i'd finished my period (it wasn't really intentional, it was just the way it rolled, i guess). within 4-5 days of each fast i would start to menstruate again. every time.
so it's hard to predict how your cycle will respond to fasting. my period has always been super-regular and it returned quickly to normal patterns after my fasts.
your body knows best. don't fear it, love it.
best of luck