A passenger on-board a Qantas plane filmed the incident in July last year, showing the lights of another plane approaching from the left, before disappearing under the wing.
Both jets were forced to abandon their landings after an Emirates passenger plane, bound for Singapore, was on the runway preparing to take-off.
With pilots given less than 20 seconds to react, Senator Nick Xenophon described the situation as a "potential disaster".
The Qantas planes were forced to perform "double go around" manoeuvres, with one jet given permission to fly across the air terminal at an unsafe altitude.
The control tower was manned by an air traffic controller trainee, a training instructor and a tower coordinator.
The trainee was serving their fourth shift in the tower and had to call a supervisor.
Mr Xenophon said he had been contacted by air traffic controllers after the incident.
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"This was a near miss," Senator Xenophon said.
"Two aircraft nearly collided in air, because of a series of systemic failures."
Melbourne's Tullamarine Airport's twin intersecting runways were highlighted as a cause for concern.
Most international airports have multiple runways, sitting parallel to one another.
Mr Xenophon also criticised commercial pressure on airports to optimise take-offs and landings, which put pressure on air traffic controllers.
Airservices Australia denied the incident had put passenger safety at risk.
SBS contacted the airport and Qantas for comment.
