Both carriers include luggage, and Rex's service will offer in-flight refreshments.
Deputy Rex chairman John Sharp said the sale would boost tourist numbers between the two major cities, which missed out on the federal government's discounted tickets measure designed to stimulate the travel industry.
"Peak tourism bodies reported yesterday that flagship stimulus programs from state and federal governments have not benefited Melbourne and Sydney," Sharp said.
"I believe this initiative will single-handedly revive a moribund travel and hospitality industry in the two cities."
Sharp noted Virgin Australia, Qantas and Jetstar were likely to play "copycat" and also reduce fares on these routes.
"Our honest prices also include our honest practices. We are the only major airline that has fully refunded all flights disrupted by Covid without resorting to disingenuous delaying tactics," he said.
The Rex figurehead also slammed Qantas over its Covid-19 refund policy, saying the airline has more than A$5bn worth of tickets waiting to be refunded.
"All the other major airlines simply do not have the cash to refund all the tickets that are entitled for a refund," Sharp said.
"Qantas, for example, has over A$5bn worth of tickets on their books, most of which are due for a refund, and its unencumbered cash is a tiny fraction of that."
Virgin said the fares include baggage, seat selection and status points.
"Virgin Australia is committed to providing travellers with some of the most competitive airfares in the market and our record low A$39 flights between Sydney and Melbourne is just one example of how irresistible it is to fly with Virgin Australia," the company said in a statement.
