The institute is housed in a purpose-built eponymous building with its iconic "cheese-grater" design created by architects Woods Bagot, located in South Australia's health and biomedical precinct on North Terrace, just east of the Royal Adelaide Hospital.

A second building (SAHMRI 2) is under construction as of August 2022, and will house the Australian Bragg Centre for Proton Therapy & Research after its completion, scheduled in late 2023.

[3] Construction of the SAHMRI 2 building, which will house the Australian Bragg Centre for Proton Therapy & Research, starts in July 2020.

[5] The operational costs of running the institute have been funded by a combination of various government grants, mainly through the National Health and Medical Research Council (for example, a total of A$34,354,553 in 2017)[7] and various other sources.

[9] In December 2018, A$12m in grant funding was announced by the government to support research in Aboriginal health, infection and immunity, and cancer.