Does the Australian Constitution define "marriage" as being between a man and a woman?

Commonwealth of Australia Constitution Act, 1900: Original Public Record Copy (1900).
Parliament House Art Collection, Art Services Parliament House
No, Section 51(xxi) of the Australian Constitution gives the Australian Parliament the power to make laws about marriage. It does not say what marriage is.
The details of how marriages are conducted in Australia are contained in the Marriage Act 1961. This law controls who can and cannot get married (for example, people who are related or under a certain age cannot get married). In 2017, gender-neutral language was introduced to allow people of the same sex to marry.