This comes after the provincial health department said it would no longer provide the hospital with an annual subsidy.
In the notice, the hospital's chief executive, Kevin Smith, says: "McCord has not received notification of an intention to renew this funding. As a result of the loss of this grant funding, McCord loses its licence to operate as a state-aided hospital and cannot afford to continue operating."
McCord is one of KwaZulu-Natal's largest hospitals, consisting of 140 beds and 400 staff. It also runs the country's biggest HIV care and treatment programme.
The hospital is scheduled to stop all healthcare services on 31 March, according to the report.
Patients will be referred to other state-funded hospitals in the city of Durban.
The province's Health MEC Sibongiseni Dhlomo declined to comment on the matter.