The Ostrovsky--Hunter equation governs evolution of shallow water waves on a
rotating fluid in the limit of small high-frequency dispersion. Sufficient
conditions for the wave breaking in the Ostrovsky--Hunter equation are found
both on an infinite line and in a periodic domain. Using the method of
characteristics, we also specify the blow-up rate at which the waves break.
Numerical illustrations of the finite-time wave breaking are given in a
periodic domain.