Australian pharmacies are running out of the medication for hyperthyroidism, a potentially life-threatening condition that affects about one in 50 people.
The TGA says the application process could take up to 10 working days, but the drug will be available sooner for patients who are seriously ill.
There is a global shortage of the drug, also known as Neo-Mercazole, which is often prescribed for people who have an overactive thyroid.
An alternative supply of the drug will not be available in pharmacies until mid-November.
Patients have been advised to work out how much of the drug they have left and then to contact their doctor to get more.
The company licensed to provide the drug, Link HealthCare, has apologised for the disruption in supply and has sourced a generic product based in Germany.