Passengers on board were "fairly stressed," said passenger Vikki Denny, a director of nursing with the Royal Flying Doctor Service.
"There were a few people around me who were fairly stressed and a baby screaming, but it was all very well controlled," she told the Adelaide Advertiser.
Denny said some people slept through the bang even despite it being loud.
The pilot on board was calm and "professional" but passengers weren't sure what was happening, she said.
"They didn't explain anything as far (as) what was occurring — they said this was an emergency procedure and there was a consistent alert going over the intercom," she told the ABC.
"The whole time we were on descent the emergency intercom was going to remain seated, keep oxygen on, this was an emergency."
Qantas has confirmed the incident was related to an issue with cabin pressurisation.
"Our pilots and cabin crew handled the incident in line with standard operating procedures," Qantas chief technical pilot Captain Alex Passerini said in a statement.
"We would like to thank our customers who followed the crew instructions and remained calm during the diversion.
"The aircraft is currently being examined by engineers in Melbourne to determine the
fault."
Passengers have been transferred to other flights while the aircraft is examined.
The Australian Transport Safety Bureau said it was gathering evidence ahead of a possible investigation.
"The ATSB can confirm it has been notified of an occurrence this morning where a Boeing 737 on a flight from Adelaide to Canberra diverted to Melbourne due to reported pressurisation issues," it said in a statement.
"The ATSB will gather information into the occurrence before making a decision on whether or not to formally investigate."
When there is pressure loss in the cabin, it's normal procedure for pilots to start a rapid descent of the plane to a safer altitude, usually no higher than 10,000 feet.
Oxygen masks drop from ceilings once the cabin pressure falls below a certain threshold. The loss of cabin pressure can be accompanied by a loud sound resembling a bang.
Last month, passengers reported being in pain and one person was bleeding from the ears as a cabin pressure problem forced the emergency landing of a Southwest flight in the United States.
In September, passengers suffered nose and ear bleeds after flight crew on a Jet Airways flight reportedly forgot to switch on the cabin pressure system.
The Boeing 737 flying from Mumbai to Jaipur, India, stopped climbing at 11,000 feet and turned back to Mumbai.
Passengers were given first aid after the plane landed safely. Passenger Satish Nair said the flight was "horrifying and the worst incident of my life."
