'immune-suppressive' is a compound formed from 'immune' and 'suppressive'. 'immune' originates from Latin 'immunis', where 'in-' meant 'not' and 'munis' meant 'obliged/dutiful' (hence 'exempt'); 'suppressive' originates from Latin 'suppressus' (past participle of 'suppressere'/'sprimere'), where 'sub-' meant 'under' and 'premere'/'primere' meant 'to press'.

'immune' entered English from Latin (via Medieval/Modern Latin and Old French influences) as a word meaning 'exempt'; 'suppressive' developed from Latin roots plus the English adjectival suffix '-ive' (formed from the verb 'suppress'). The modern compound 'immune-suppressive' arose in 20th-century medical English by combining these elements to describe agents or effects that suppress immunity.

Initially, 'immune' meant 'exempt' and 'suppressive' meant 'pressing down'; combined in modern medical usage they mean 'causing suppression of the immune system' or 'tending to reduce immune function'.