'toxically' originates from English, specifically the adjective 'toxic', where 'toxic' meant 'poisonous or harmful'.

'toxic' entered English from Late Latin 'toxicus' and Latin 'toxicum', which in turn came from Greek 'toxikon (pharmakon)'; the Greek root 'toxon' originally meant 'bow' and 'toxikon' came to mean 'poison for arrows.' Over time the form developed into the modern English 'toxic' and then the adverb 'toxically'.

Initially it referred narrowly to poisons (especially arrow-poisons); over time it broadened to mean 'poisonous' or generally 'harmful', and later extended figuratively to describe harmful behavior or environments—hence 'toxically' meaning 'in a harmful/poisonous way'.