Whether or not other mammals menstruate may depend on your exact definition of the term. Chimpanzees certainly do (and, indeed, rarely experience menopause), and it's present to a variable extent in other apes and Old World monkeys. In New World monkeys it's microscopic and it's completely absent in lemurs. At least some bats menstruate, as do sengis (elephant shrews) and, so far as we know, just one species of rodent.