"the Brasilians take no physick but their tobacco"
Nicotiana tabacum plant
Creative Commons Attribution Share AlikeNicotiana tabacum plant - Credit: Joachim Muellerchen

Smoking tobacco to cure illnesses was based on the idea that the ‘humours’ of the body needed to be balanced: tobacco was thought to "evacuate" an excess of humours, much like letting blood.  Andre Thevet wrote in 1568 that the people of Brazil smoked tobacco to clear the "superfluous humours of the brain".

More information can be found in Geoffrey M Sill’s ‘A Source for Crusoe’s Tobacco Cure’, English Language Notes 32.4 (1995), pp. 46-8.