Other procedures to restart after the Anzac Day long weekend include all children surgeries, joint replacements, eye procedures, endoscopy and colonoscopy.
It amounts to category two procedures as well as some category three.
Mr Morrison said national cabinet will review the decision on 11 May, to decide if all elective surgeries should begin again.
"Priority will be given ... on the basis of clinical determinations by the relevant health professionals and that will occur in both the public and private system," he told reporters in Canberra.
"This is an important decision because it marks another step on the way back. There is a road back."
A shipment of 58 million face masks was recently received by the Federal Government.
Health Minister Greg Hunt said another 100 million will arrive over the next six weeks.
As well, the goal of securing 7,500 ventilators had been reached.
"[This will make] an immense difference for families, whether it is in terms of IVF, dental pain or orthopaedic procedures .... it will mean a difference to the quality of life," Mr Hunt said.
People in Australia must stay at least 1.5 metres away from others and gatherings are limited to two people unless you are with your family or household.
If you believe you may have contracted the virus, call your doctor (don’t visit) or contact the national Coronavirus Health Information Hotline on 1800 020 080. If you are struggling to breathe or experiencing a medical emergency, call 000.
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